Calculate and Count All the Factors of 81,818,100. Online Calculator

All the factors (divisors) of the number 81,818,100. How important is the prime factorization of the number

1. Carry out the prime factorization of the number 81,818,100:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

81,818,100 = 22 × 35 × 52 × 7 × 13 × 37
81,818,100 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers (decomposition into prime factors)

* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


How to count the number of factors of a number?

If a number N is prime factorized as:
N = am × bk × cz
where a, b, c are the prime factors and m, k, z are their exponents, natural numbers, ....

Then the number of factors of the number N can be calculated as:
n = (m + 1) × (k + 1) × (z + 1)

In our case, the number of factors is calculated as:

n = (2 + 1) × (5 + 1) × (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 6 × 3 × 2 × 2 × 2 = 432

But to actually calculate the factors, see below...

2. Multiply the prime factors of the number 81,818,100

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.

Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
prime factor = 7
32 = 9
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
52 = 25
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
5 × 7 = 35
22 × 32 = 36
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
32 × 5 = 45
2 × 52 = 50
22 × 13 = 52
2 × 33 = 54
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 5 × 7 = 70
2 × 37 = 74
3 × 52 = 75
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
22 × 52 = 100
3 × 5 × 7 = 105
22 × 33 = 108
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
22 × 5 × 7 = 140
22 × 37 = 148
2 × 3 × 52 = 150
22 × 3 × 13 = 156
2 × 34 = 162
52 × 7 = 175
22 × 32 × 5 = 180
2 × 7 × 13 = 182
5 × 37 = 185
33 × 7 = 189
3 × 5 × 13 = 195
2 × 3 × 5 × 7 = 210
2 × 3 × 37 = 222
32 × 52 = 225
2 × 32 × 13 = 234
35 = 243
22 × 32 × 7 = 252
7 × 37 = 259
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
22 × 3 × 52 = 300
32 × 5 × 7 = 315
22 × 34 = 324
52 × 13 = 325
32 × 37 = 333
2 × 52 × 7 = 350
33 × 13 = 351
22 × 7 × 13 = 364
2 × 5 × 37 = 370
2 × 33 × 7 = 378
2 × 3 × 5 × 13 = 390
34 × 5 = 405
22 × 3 × 5 × 7 = 420
22 × 3 × 37 = 444
2 × 32 × 52 = 450
5 × 7 × 13 = 455
22 × 32 × 13 = 468
13 × 37 = 481
2 × 35 = 486
2 × 7 × 37 = 518
3 × 52 × 7 = 525
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
3 × 5 × 37 = 555
34 × 7 = 567
32 × 5 × 13 = 585
2 × 32 × 5 × 7 = 630
2 × 52 × 13 = 650
2 × 32 × 37 = 666
33 × 52 = 675
22 × 52 × 7 = 700
2 × 33 × 13 = 702
22 × 5 × 37 = 740
22 × 33 × 7 = 756
3 × 7 × 37 = 777
22 × 3 × 5 × 13 = 780
2 × 34 × 5 = 810
32 × 7 × 13 = 819
22 × 32 × 52 = 900
2 × 5 × 7 × 13 = 910
52 × 37 = 925
33 × 5 × 7 = 945
2 × 13 × 37 = 962
22 × 35 = 972
3 × 52 × 13 = 975
33 × 37 = 999
22 × 7 × 37 = 1,036
2 × 3 × 52 × 7 = 1,050
34 × 13 = 1,053
22 × 3 × 7 × 13 = 1,092
2 × 3 × 5 × 37 = 1,110
2 × 34 × 7 = 1,134
2 × 32 × 5 × 13 = 1,170
35 × 5 = 1,215
22 × 32 × 5 × 7 = 1,260
5 × 7 × 37 = 1,295
22 × 52 × 13 = 1,300
22 × 32 × 37 = 1,332
2 × 33 × 52 = 1,350
3 × 5 × 7 × 13 = 1,365
22 × 33 × 13 = 1,404
3 × 13 × 37 = 1,443
2 × 3 × 7 × 37 = 1,554
32 × 52 × 7 = 1,575
22 × 34 × 5 = 1,620
2 × 32 × 7 × 13 = 1,638
32 × 5 × 37 = 1,665
35 × 7 = 1,701
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
2 × 52 × 37 = 1,850
2 × 33 × 5 × 7 = 1,890
22 × 13 × 37 = 1,924
2 × 3 × 52 × 13 = 1,950
2 × 33 × 37 = 1,998
34 × 52 = 2,025
22 × 3 × 52 × 7 = 2,100
2 × 34 × 13 = 2,106
22 × 3 × 5 × 37 = 2,220
22 × 34 × 7 = 2,268
52 × 7 × 13 = 2,275
32 × 7 × 37 = 2,331
22 × 32 × 5 × 13 = 2,340
5 × 13 × 37 = 2,405
2 × 35 × 5 = 2,430
33 × 7 × 13 = 2,457
2 × 5 × 7 × 37 = 2,590
22 × 33 × 52 = 2,700
2 × 3 × 5 × 7 × 13 = 2,730
3 × 52 × 37 = 2,775
34 × 5 × 7 = 2,835
2 × 3 × 13 × 37 = 2,886
32 × 52 × 13 = 2,925
34 × 37 = 2,997
22 × 3 × 7 × 37 = 3,108
2 × 32 × 52 × 7 = 3,150
35 × 13 = 3,159
22 × 32 × 7 × 13 = 3,276
2 × 32 × 5 × 37 = 3,330
7 × 13 × 37 = 3,367
2 × 35 × 7 = 3,402
2 × 33 × 5 × 13 = 3,510
22 × 52 × 37 = 3,700
22 × 33 × 5 × 7 = 3,780
3 × 5 × 7 × 37 = 3,885
22 × 3 × 52 × 13 = 3,900
22 × 33 × 37 = 3,996
2 × 34 × 52 = 4,050
32 × 5 × 7 × 13 = 4,095
22 × 34 × 13 = 4,212
32 × 13 × 37 = 4,329
2 × 52 × 7 × 13 = 4,550
2 × 32 × 7 × 37 = 4,662
33 × 52 × 7 = 4,725
2 × 5 × 13 × 37 = 4,810
22 × 35 × 5 = 4,860
2 × 33 × 7 × 13 = 4,914
33 × 5 × 37 = 4,995
22 × 5 × 7 × 37 = 5,180
34 × 5 × 13 = 5,265
22 × 3 × 5 × 7 × 13 = 5,460
2 × 3 × 52 × 37 = 5,550
2 × 34 × 5 × 7 = 5,670
22 × 3 × 13 × 37 = 5,772
2 × 32 × 52 × 13 = 5,850
2 × 34 × 37 = 5,994
35 × 52 = 6,075
22 × 32 × 52 × 7 = 6,300
2 × 35 × 13 = 6,318
52 × 7 × 37 = 6,475
22 × 32 × 5 × 37 = 6,660
2 × 7 × 13 × 37 = 6,734
22 × 35 × 7 = 6,804
3 × 52 × 7 × 13 = 6,825
33 × 7 × 37 = 6,993
22 × 33 × 5 × 13 = 7,020
3 × 5 × 13 × 37 = 7,215
34 × 7 × 13 = 7,371
2 × 3 × 5 × 7 × 37 = 7,770
22 × 34 × 52 = 8,100
2 × 32 × 5 × 7 × 13 = 8,190
32 × 52 × 37 = 8,325
35 × 5 × 7 = 8,505
2 × 32 × 13 × 37 = 8,658
33 × 52 × 13 = 8,775
35 × 37 = 8,991
This list continues below...

... This list continues from above
22 × 52 × 7 × 13 = 9,100
22 × 32 × 7 × 37 = 9,324
2 × 33 × 52 × 7 = 9,450
22 × 5 × 13 × 37 = 9,620
22 × 33 × 7 × 13 = 9,828
2 × 33 × 5 × 37 = 9,990
3 × 7 × 13 × 37 = 10,101
2 × 34 × 5 × 13 = 10,530
22 × 3 × 52 × 37 = 11,100
22 × 34 × 5 × 7 = 11,340
32 × 5 × 7 × 37 = 11,655
22 × 32 × 52 × 13 = 11,700
22 × 34 × 37 = 11,988
52 × 13 × 37 = 12,025
2 × 35 × 52 = 12,150
33 × 5 × 7 × 13 = 12,285
22 × 35 × 13 = 12,636
2 × 52 × 7 × 37 = 12,950
33 × 13 × 37 = 12,987
22 × 7 × 13 × 37 = 13,468
2 × 3 × 52 × 7 × 13 = 13,650
2 × 33 × 7 × 37 = 13,986
34 × 52 × 7 = 14,175
2 × 3 × 5 × 13 × 37 = 14,430
2 × 34 × 7 × 13 = 14,742
34 × 5 × 37 = 14,985
22 × 3 × 5 × 7 × 37 = 15,540
35 × 5 × 13 = 15,795
22 × 32 × 5 × 7 × 13 = 16,380
2 × 32 × 52 × 37 = 16,650
5 × 7 × 13 × 37 = 16,835
2 × 35 × 5 × 7 = 17,010
22 × 32 × 13 × 37 = 17,316
2 × 33 × 52 × 13 = 17,550
2 × 35 × 37 = 17,982
22 × 33 × 52 × 7 = 18,900
3 × 52 × 7 × 37 = 19,425
22 × 33 × 5 × 37 = 19,980
2 × 3 × 7 × 13 × 37 = 20,202
32 × 52 × 7 × 13 = 20,475
34 × 7 × 37 = 20,979
22 × 34 × 5 × 13 = 21,060
32 × 5 × 13 × 37 = 21,645
35 × 7 × 13 = 22,113
2 × 32 × 5 × 7 × 37 = 23,310
2 × 52 × 13 × 37 = 24,050
22 × 35 × 52 = 24,300
2 × 33 × 5 × 7 × 13 = 24,570
33 × 52 × 37 = 24,975
22 × 52 × 7 × 37 = 25,900
2 × 33 × 13 × 37 = 25,974
34 × 52 × 13 = 26,325
22 × 3 × 52 × 7 × 13 = 27,300
22 × 33 × 7 × 37 = 27,972
2 × 34 × 52 × 7 = 28,350
22 × 3 × 5 × 13 × 37 = 28,860
22 × 34 × 7 × 13 = 29,484
2 × 34 × 5 × 37 = 29,970
32 × 7 × 13 × 37 = 30,303
2 × 35 × 5 × 13 = 31,590
22 × 32 × 52 × 37 = 33,300
2 × 5 × 7 × 13 × 37 = 33,670
22 × 35 × 5 × 7 = 34,020
33 × 5 × 7 × 37 = 34,965
22 × 33 × 52 × 13 = 35,100
22 × 35 × 37 = 35,964
3 × 52 × 13 × 37 = 36,075
34 × 5 × 7 × 13 = 36,855
2 × 3 × 52 × 7 × 37 = 38,850
34 × 13 × 37 = 38,961
22 × 3 × 7 × 13 × 37 = 40,404
2 × 32 × 52 × 7 × 13 = 40,950
2 × 34 × 7 × 37 = 41,958
35 × 52 × 7 = 42,525
2 × 32 × 5 × 13 × 37 = 43,290
2 × 35 × 7 × 13 = 44,226
35 × 5 × 37 = 44,955
22 × 32 × 5 × 7 × 37 = 46,620
22 × 52 × 13 × 37 = 48,100
22 × 33 × 5 × 7 × 13 = 49,140
2 × 33 × 52 × 37 = 49,950
3 × 5 × 7 × 13 × 37 = 50,505
22 × 33 × 13 × 37 = 51,948
2 × 34 × 52 × 13 = 52,650
22 × 34 × 52 × 7 = 56,700
32 × 52 × 7 × 37 = 58,275
22 × 34 × 5 × 37 = 59,940
2 × 32 × 7 × 13 × 37 = 60,606
33 × 52 × 7 × 13 = 61,425
35 × 7 × 37 = 62,937
22 × 35 × 5 × 13 = 63,180
33 × 5 × 13 × 37 = 64,935
22 × 5 × 7 × 13 × 37 = 67,340
2 × 33 × 5 × 7 × 37 = 69,930
2 × 3 × 52 × 13 × 37 = 72,150
2 × 34 × 5 × 7 × 13 = 73,710
34 × 52 × 37 = 74,925
22 × 3 × 52 × 7 × 37 = 77,700
2 × 34 × 13 × 37 = 77,922
35 × 52 × 13 = 78,975
22 × 32 × 52 × 7 × 13 = 81,900
22 × 34 × 7 × 37 = 83,916
52 × 7 × 13 × 37 = 84,175
2 × 35 × 52 × 7 = 85,050
22 × 32 × 5 × 13 × 37 = 86,580
22 × 35 × 7 × 13 = 88,452
2 × 35 × 5 × 37 = 89,910
33 × 7 × 13 × 37 = 90,909
22 × 33 × 52 × 37 = 99,900
2 × 3 × 5 × 7 × 13 × 37 = 101,010
34 × 5 × 7 × 37 = 104,895
22 × 34 × 52 × 13 = 105,300
32 × 52 × 13 × 37 = 108,225
35 × 5 × 7 × 13 = 110,565
2 × 32 × 52 × 7 × 37 = 116,550
35 × 13 × 37 = 116,883
22 × 32 × 7 × 13 × 37 = 121,212
2 × 33 × 52 × 7 × 13 = 122,850
2 × 35 × 7 × 37 = 125,874
2 × 33 × 5 × 13 × 37 = 129,870
22 × 33 × 5 × 7 × 37 = 139,860
22 × 3 × 52 × 13 × 37 = 144,300
22 × 34 × 5 × 7 × 13 = 147,420
2 × 34 × 52 × 37 = 149,850
32 × 5 × 7 × 13 × 37 = 151,515
22 × 34 × 13 × 37 = 155,844
2 × 35 × 52 × 13 = 157,950
2 × 52 × 7 × 13 × 37 = 168,350
22 × 35 × 52 × 7 = 170,100
33 × 52 × 7 × 37 = 174,825
22 × 35 × 5 × 37 = 179,820
2 × 33 × 7 × 13 × 37 = 181,818
34 × 52 × 7 × 13 = 184,275
34 × 5 × 13 × 37 = 194,805
22 × 3 × 5 × 7 × 13 × 37 = 202,020
2 × 34 × 5 × 7 × 37 = 209,790
2 × 32 × 52 × 13 × 37 = 216,450
2 × 35 × 5 × 7 × 13 = 221,130
35 × 52 × 37 = 224,775
22 × 32 × 52 × 7 × 37 = 233,100
2 × 35 × 13 × 37 = 233,766
22 × 33 × 52 × 7 × 13 = 245,700
22 × 35 × 7 × 37 = 251,748
3 × 52 × 7 × 13 × 37 = 252,525
22 × 33 × 5 × 13 × 37 = 259,740
34 × 7 × 13 × 37 = 272,727
22 × 34 × 52 × 37 = 299,700
2 × 32 × 5 × 7 × 13 × 37 = 303,030
35 × 5 × 7 × 37 = 314,685
22 × 35 × 52 × 13 = 315,900
33 × 52 × 13 × 37 = 324,675
22 × 52 × 7 × 13 × 37 = 336,700
2 × 33 × 52 × 7 × 37 = 349,650
22 × 33 × 7 × 13 × 37 = 363,636
2 × 34 × 52 × 7 × 13 = 368,550
2 × 34 × 5 × 13 × 37 = 389,610
22 × 34 × 5 × 7 × 37 = 419,580
22 × 32 × 52 × 13 × 37 = 432,900
22 × 35 × 5 × 7 × 13 = 442,260
2 × 35 × 52 × 37 = 449,550
33 × 5 × 7 × 13 × 37 = 454,545
22 × 35 × 13 × 37 = 467,532
2 × 3 × 52 × 7 × 13 × 37 = 505,050
34 × 52 × 7 × 37 = 524,475
2 × 34 × 7 × 13 × 37 = 545,454
35 × 52 × 7 × 13 = 552,825
35 × 5 × 13 × 37 = 584,415
22 × 32 × 5 × 7 × 13 × 37 = 606,060
2 × 35 × 5 × 7 × 37 = 629,370
2 × 33 × 52 × 13 × 37 = 649,350
22 × 33 × 52 × 7 × 37 = 699,300
22 × 34 × 52 × 7 × 13 = 737,100
32 × 52 × 7 × 13 × 37 = 757,575
22 × 34 × 5 × 13 × 37 = 779,220
35 × 7 × 13 × 37 = 818,181
22 × 35 × 52 × 37 = 899,100
2 × 33 × 5 × 7 × 13 × 37 = 909,090
34 × 52 × 13 × 37 = 974,025
22 × 3 × 52 × 7 × 13 × 37 = 1,010,100
2 × 34 × 52 × 7 × 37 = 1,048,950
22 × 34 × 7 × 13 × 37 = 1,090,908
2 × 35 × 52 × 7 × 13 = 1,105,650
2 × 35 × 5 × 13 × 37 = 1,168,830
22 × 35 × 5 × 7 × 37 = 1,258,740
22 × 33 × 52 × 13 × 37 = 1,298,700
34 × 5 × 7 × 13 × 37 = 1,363,635
2 × 32 × 52 × 7 × 13 × 37 = 1,515,150
35 × 52 × 7 × 37 = 1,573,425
2 × 35 × 7 × 13 × 37 = 1,636,362
22 × 33 × 5 × 7 × 13 × 37 = 1,818,180
2 × 34 × 52 × 13 × 37 = 1,948,050
22 × 34 × 52 × 7 × 37 = 2,097,900
22 × 35 × 52 × 7 × 13 = 2,211,300
33 × 52 × 7 × 13 × 37 = 2,272,725
22 × 35 × 5 × 13 × 37 = 2,337,660
2 × 34 × 5 × 7 × 13 × 37 = 2,727,270
35 × 52 × 13 × 37 = 2,922,075
22 × 32 × 52 × 7 × 13 × 37 = 3,030,300
2 × 35 × 52 × 7 × 37 = 3,146,850
22 × 35 × 7 × 13 × 37 = 3,272,724
22 × 34 × 52 × 13 × 37 = 3,896,100
35 × 5 × 7 × 13 × 37 = 4,090,905
2 × 33 × 52 × 7 × 13 × 37 = 4,545,450
22 × 34 × 5 × 7 × 13 × 37 = 5,454,540
2 × 35 × 52 × 13 × 37 = 5,844,150
22 × 35 × 52 × 7 × 37 = 6,293,700
34 × 52 × 7 × 13 × 37 = 6,818,175
2 × 35 × 5 × 7 × 13 × 37 = 8,181,810
22 × 33 × 52 × 7 × 13 × 37 = 9,090,900
22 × 35 × 52 × 13 × 37 = 11,688,300
2 × 34 × 52 × 7 × 13 × 37 = 13,636,350
22 × 35 × 5 × 7 × 13 × 37 = 16,363,620
35 × 52 × 7 × 13 × 37 = 20,454,525
22 × 34 × 52 × 7 × 13 × 37 = 27,272,700
2 × 35 × 52 × 7 × 13 × 37 = 40,909,050
22 × 35 × 52 × 7 × 13 × 37 = 81,818,100

The final answer:
(scroll down)

81,818,100 has 432 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 12; 13; 14; 15; 18; 20; 21; 25; 26; 27; 28; 30; 35; 36; 37; 39; 42; 45; 50; 52; 54; 60; 63; 65; 70; 74; 75; 78; 81; 84; 90; 91; 100; 105; 108; 111; 117; 126; 130; 135; 140; 148; 150; 156; 162; 175; 180; 182; 185; 189; 195; 210; 222; 225; 234; 243; 252; 259; 260; 270; 273; 300; 315; 324; 325; 333; 350; 351; 364; 370; 378; 390; 405; 420; 444; 450; 455; 468; 481; 486; 518; 525; 540; 546; 555; 567; 585; 630; 650; 666; 675; 700; 702; 740; 756; 777; 780; 810; 819; 900; 910; 925; 945; 962; 972; 975; 999; 1,036; 1,050; 1,053; 1,092; 1,110; 1,134; 1,170; 1,215; 1,260; 1,295; 1,300; 1,332; 1,350; 1,365; 1,404; 1,443; 1,554; 1,575; 1,620; 1,638; 1,665; 1,701; 1,755; 1,820; 1,850; 1,890; 1,924; 1,950; 1,998; 2,025; 2,100; 2,106; 2,220; 2,268; 2,275; 2,331; 2,340; 2,405; 2,430; 2,457; 2,590; 2,700; 2,730; 2,775; 2,835; 2,886; 2,925; 2,997; 3,108; 3,150; 3,159; 3,276; 3,330; 3,367; 3,402; 3,510; 3,700; 3,780; 3,885; 3,900; 3,996; 4,050; 4,095; 4,212; 4,329; 4,550; 4,662; 4,725; 4,810; 4,860; 4,914; 4,995; 5,180; 5,265; 5,460; 5,550; 5,670; 5,772; 5,850; 5,994; 6,075; 6,300; 6,318; 6,475; 6,660; 6,734; 6,804; 6,825; 6,993; 7,020; 7,215; 7,371; 7,770; 8,100; 8,190; 8,325; 8,505; 8,658; 8,775; 8,991; 9,100; 9,324; 9,450; 9,620; 9,828; 9,990; 10,101; 10,530; 11,100; 11,340; 11,655; 11,700; 11,988; 12,025; 12,150; 12,285; 12,636; 12,950; 12,987; 13,468; 13,650; 13,986; 14,175; 14,430; 14,742; 14,985; 15,540; 15,795; 16,380; 16,650; 16,835; 17,010; 17,316; 17,550; 17,982; 18,900; 19,425; 19,980; 20,202; 20,475; 20,979; 21,060; 21,645; 22,113; 23,310; 24,050; 24,300; 24,570; 24,975; 25,900; 25,974; 26,325; 27,300; 27,972; 28,350; 28,860; 29,484; 29,970; 30,303; 31,590; 33,300; 33,670; 34,020; 34,965; 35,100; 35,964; 36,075; 36,855; 38,850; 38,961; 40,404; 40,950; 41,958; 42,525; 43,290; 44,226; 44,955; 46,620; 48,100; 49,140; 49,950; 50,505; 51,948; 52,650; 56,700; 58,275; 59,940; 60,606; 61,425; 62,937; 63,180; 64,935; 67,340; 69,930; 72,150; 73,710; 74,925; 77,700; 77,922; 78,975; 81,900; 83,916; 84,175; 85,050; 86,580; 88,452; 89,910; 90,909; 99,900; 101,010; 104,895; 105,300; 108,225; 110,565; 116,550; 116,883; 121,212; 122,850; 125,874; 129,870; 139,860; 144,300; 147,420; 149,850; 151,515; 155,844; 157,950; 168,350; 170,100; 174,825; 179,820; 181,818; 184,275; 194,805; 202,020; 209,790; 216,450; 221,130; 224,775; 233,100; 233,766; 245,700; 251,748; 252,525; 259,740; 272,727; 299,700; 303,030; 314,685; 315,900; 324,675; 336,700; 349,650; 363,636; 368,550; 389,610; 419,580; 432,900; 442,260; 449,550; 454,545; 467,532; 505,050; 524,475; 545,454; 552,825; 584,415; 606,060; 629,370; 649,350; 699,300; 737,100; 757,575; 779,220; 818,181; 899,100; 909,090; 974,025; 1,010,100; 1,048,950; 1,090,908; 1,105,650; 1,168,830; 1,258,740; 1,298,700; 1,363,635; 1,515,150; 1,573,425; 1,636,362; 1,818,180; 1,948,050; 2,097,900; 2,211,300; 2,272,725; 2,337,660; 2,727,270; 2,922,075; 3,030,300; 3,146,850; 3,272,724; 3,896,100; 4,090,905; 4,545,450; 5,454,540; 5,844,150; 6,293,700; 6,818,175; 8,181,810; 9,090,900; 11,688,300; 13,636,350; 16,363,620; 20,454,525; 27,272,700; 40,909,050 and 81,818,100
out of which 6 prime factors: 2; 3; 5; 7; 13 and 37
81,818,100 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.

Then multiply the prime factors and their exponents, if any, in all their different combinations.


Other similar operations of calculating common factors:

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Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

  • If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
  • The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).
  • Factors of the GCF
  • If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".