Given the Number 33,333,300 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 33,333,300

1. Carry out the prime factorization of the number 33,333,300:

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


33,333,300 = 22 × 32 × 52 × 7 × 11 × 13 × 37
33,333,300 is not a prime number but a composite one.


* 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.


2. Multiply the prime factors of the number 33,333,300

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
prime factor = 11
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
2 × 11 = 22
52 = 25
2 × 13 = 26
22 × 7 = 28
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
22 × 32 = 36
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
22 × 11 = 44
32 × 5 = 45
2 × 52 = 50
22 × 13 = 52
5 × 11 = 55
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 3 × 11 = 66
2 × 5 × 7 = 70
2 × 37 = 74
3 × 52 = 75
7 × 11 = 77
2 × 3 × 13 = 78
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
32 × 11 = 99
22 × 52 = 100
3 × 5 × 7 = 105
2 × 5 × 11 = 110
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
22 × 3 × 11 = 132
22 × 5 × 7 = 140
11 × 13 = 143
22 × 37 = 148
2 × 3 × 52 = 150
2 × 7 × 11 = 154
22 × 3 × 13 = 156
3 × 5 × 11 = 165
52 × 7 = 175
22 × 32 × 5 = 180
2 × 7 × 13 = 182
5 × 37 = 185
3 × 5 × 13 = 195
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
22 × 5 × 11 = 220
2 × 3 × 37 = 222
32 × 52 = 225
3 × 7 × 11 = 231
2 × 32 × 13 = 234
22 × 32 × 7 = 252
7 × 37 = 259
22 × 5 × 13 = 260
3 × 7 × 13 = 273
52 × 11 = 275
2 × 11 × 13 = 286
22 × 3 × 52 = 300
22 × 7 × 11 = 308
32 × 5 × 7 = 315
52 × 13 = 325
2 × 3 × 5 × 11 = 330
32 × 37 = 333
2 × 52 × 7 = 350
22 × 7 × 13 = 364
2 × 5 × 37 = 370
5 × 7 × 11 = 385
2 × 3 × 5 × 13 = 390
22 × 32 × 11 = 396
11 × 37 = 407
22 × 3 × 5 × 7 = 420
3 × 11 × 13 = 429
22 × 3 × 37 = 444
2 × 32 × 52 = 450
5 × 7 × 13 = 455
2 × 3 × 7 × 11 = 462
22 × 32 × 13 = 468
13 × 37 = 481
32 × 5 × 11 = 495
2 × 7 × 37 = 518
3 × 52 × 7 = 525
2 × 3 × 7 × 13 = 546
2 × 52 × 11 = 550
3 × 5 × 37 = 555
22 × 11 × 13 = 572
32 × 5 × 13 = 585
2 × 32 × 5 × 7 = 630
2 × 52 × 13 = 650
22 × 3 × 5 × 11 = 660
2 × 32 × 37 = 666
32 × 7 × 11 = 693
22 × 52 × 7 = 700
5 × 11 × 13 = 715
22 × 5 × 37 = 740
2 × 5 × 7 × 11 = 770
3 × 7 × 37 = 777
22 × 3 × 5 × 13 = 780
2 × 11 × 37 = 814
32 × 7 × 13 = 819
3 × 52 × 11 = 825
2 × 3 × 11 × 13 = 858
22 × 32 × 52 = 900
2 × 5 × 7 × 13 = 910
22 × 3 × 7 × 11 = 924
52 × 37 = 925
2 × 13 × 37 = 962
3 × 52 × 13 = 975
2 × 32 × 5 × 11 = 990
7 × 11 × 13 = 1,001
22 × 7 × 37 = 1,036
2 × 3 × 52 × 7 = 1,050
22 × 3 × 7 × 13 = 1,092
22 × 52 × 11 = 1,100
2 × 3 × 5 × 37 = 1,110
3 × 5 × 7 × 11 = 1,155
2 × 32 × 5 × 13 = 1,170
3 × 11 × 37 = 1,221
22 × 32 × 5 × 7 = 1,260
32 × 11 × 13 = 1,287
5 × 7 × 37 = 1,295
22 × 52 × 13 = 1,300
22 × 32 × 37 = 1,332
3 × 5 × 7 × 13 = 1,365
2 × 32 × 7 × 11 = 1,386
2 × 5 × 11 × 13 = 1,430
3 × 13 × 37 = 1,443
22 × 5 × 7 × 11 = 1,540
2 × 3 × 7 × 37 = 1,554
32 × 52 × 7 = 1,575
22 × 11 × 37 = 1,628
2 × 32 × 7 × 13 = 1,638
2 × 3 × 52 × 11 = 1,650
32 × 5 × 37 = 1,665
22 × 3 × 11 × 13 = 1,716
22 × 5 × 7 × 13 = 1,820
2 × 52 × 37 = 1,850
22 × 13 × 37 = 1,924
52 × 7 × 11 = 1,925
2 × 3 × 52 × 13 = 1,950
22 × 32 × 5 × 11 = 1,980
2 × 7 × 11 × 13 = 2,002
5 × 11 × 37 = 2,035
22 × 3 × 52 × 7 = 2,100
3 × 5 × 11 × 13 = 2,145
22 × 3 × 5 × 37 = 2,220
52 × 7 × 13 = 2,275
2 × 3 × 5 × 7 × 11 = 2,310
32 × 7 × 37 = 2,331
22 × 32 × 5 × 13 = 2,340
5 × 13 × 37 = 2,405
2 × 3 × 11 × 37 = 2,442
32 × 52 × 11 = 2,475
2 × 32 × 11 × 13 = 2,574
2 × 5 × 7 × 37 = 2,590
2 × 3 × 5 × 7 × 13 = 2,730
22 × 32 × 7 × 11 = 2,772
3 × 52 × 37 = 2,775
7 × 11 × 37 = 2,849
22 × 5 × 11 × 13 = 2,860
2 × 3 × 13 × 37 = 2,886
32 × 52 × 13 = 2,925
3 × 7 × 11 × 13 = 3,003
22 × 3 × 7 × 37 = 3,108
2 × 32 × 52 × 7 = 3,150
22 × 32 × 7 × 13 = 3,276
22 × 3 × 52 × 11 = 3,300
2 × 32 × 5 × 37 = 3,330
7 × 13 × 37 = 3,367
32 × 5 × 7 × 11 = 3,465
52 × 11 × 13 = 3,575
32 × 11 × 37 = 3,663
22 × 52 × 37 = 3,700
2 × 52 × 7 × 11 = 3,850
3 × 5 × 7 × 37 = 3,885
22 × 3 × 52 × 13 = 3,900
22 × 7 × 11 × 13 = 4,004
2 × 5 × 11 × 37 = 4,070
32 × 5 × 7 × 13 = 4,095
2 × 3 × 5 × 11 × 13 = 4,290
32 × 13 × 37 = 4,329
2 × 52 × 7 × 13 = 4,550
22 × 3 × 5 × 7 × 11 = 4,620
2 × 32 × 7 × 37 = 4,662
2 × 5 × 13 × 37 = 4,810
22 × 3 × 11 × 37 = 4,884
2 × 32 × 52 × 11 = 4,950
5 × 7 × 11 × 13 = 5,005
22 × 32 × 11 × 13 = 5,148
22 × 5 × 7 × 37 = 5,180
11 × 13 × 37 = 5,291
22 × 3 × 5 × 7 × 13 = 5,460
2 × 3 × 52 × 37 = 5,550
2 × 7 × 11 × 37 = 5,698
22 × 3 × 13 × 37 = 5,772
This list continues below...

... This list continues from above
3 × 52 × 7 × 11 = 5,775
2 × 32 × 52 × 13 = 5,850
2 × 3 × 7 × 11 × 13 = 6,006
3 × 5 × 11 × 37 = 6,105
22 × 32 × 52 × 7 = 6,300
32 × 5 × 11 × 13 = 6,435
52 × 7 × 37 = 6,475
22 × 32 × 5 × 37 = 6,660
2 × 7 × 13 × 37 = 6,734
3 × 52 × 7 × 13 = 6,825
2 × 32 × 5 × 7 × 11 = 6,930
2 × 52 × 11 × 13 = 7,150
3 × 5 × 13 × 37 = 7,215
2 × 32 × 11 × 37 = 7,326
22 × 52 × 7 × 11 = 7,700
2 × 3 × 5 × 7 × 37 = 7,770
22 × 5 × 11 × 37 = 8,140
2 × 32 × 5 × 7 × 13 = 8,190
32 × 52 × 37 = 8,325
3 × 7 × 11 × 37 = 8,547
22 × 3 × 5 × 11 × 13 = 8,580
2 × 32 × 13 × 37 = 8,658
32 × 7 × 11 × 13 = 9,009
22 × 52 × 7 × 13 = 9,100
22 × 32 × 7 × 37 = 9,324
22 × 5 × 13 × 37 = 9,620
22 × 32 × 52 × 11 = 9,900
2 × 5 × 7 × 11 × 13 = 10,010
3 × 7 × 13 × 37 = 10,101
52 × 11 × 37 = 10,175
2 × 11 × 13 × 37 = 10,582
3 × 52 × 11 × 13 = 10,725
22 × 3 × 52 × 37 = 11,100
22 × 7 × 11 × 37 = 11,396
2 × 3 × 52 × 7 × 11 = 11,550
32 × 5 × 7 × 37 = 11,655
22 × 32 × 52 × 13 = 11,700
22 × 3 × 7 × 11 × 13 = 12,012
52 × 13 × 37 = 12,025
2 × 3 × 5 × 11 × 37 = 12,210
2 × 32 × 5 × 11 × 13 = 12,870
2 × 52 × 7 × 37 = 12,950
22 × 7 × 13 × 37 = 13,468
2 × 3 × 52 × 7 × 13 = 13,650
22 × 32 × 5 × 7 × 11 = 13,860
5 × 7 × 11 × 37 = 14,245
22 × 52 × 11 × 13 = 14,300
2 × 3 × 5 × 13 × 37 = 14,430
22 × 32 × 11 × 37 = 14,652
3 × 5 × 7 × 11 × 13 = 15,015
22 × 3 × 5 × 7 × 37 = 15,540
3 × 11 × 13 × 37 = 15,873
22 × 32 × 5 × 7 × 13 = 16,380
2 × 32 × 52 × 37 = 16,650
5 × 7 × 13 × 37 = 16,835
2 × 3 × 7 × 11 × 37 = 17,094
22 × 32 × 13 × 37 = 17,316
32 × 52 × 7 × 11 = 17,325
2 × 32 × 7 × 11 × 13 = 18,018
32 × 5 × 11 × 37 = 18,315
3 × 52 × 7 × 37 = 19,425
22 × 5 × 7 × 11 × 13 = 20,020
2 × 3 × 7 × 13 × 37 = 20,202
2 × 52 × 11 × 37 = 20,350
32 × 52 × 7 × 13 = 20,475
22 × 11 × 13 × 37 = 21,164
2 × 3 × 52 × 11 × 13 = 21,450
32 × 5 × 13 × 37 = 21,645
22 × 3 × 52 × 7 × 11 = 23,100
2 × 32 × 5 × 7 × 37 = 23,310
2 × 52 × 13 × 37 = 24,050
22 × 3 × 5 × 11 × 37 = 24,420
52 × 7 × 11 × 13 = 25,025
32 × 7 × 11 × 37 = 25,641
22 × 32 × 5 × 11 × 13 = 25,740
22 × 52 × 7 × 37 = 25,900
5 × 11 × 13 × 37 = 26,455
22 × 3 × 52 × 7 × 13 = 27,300
2 × 5 × 7 × 11 × 37 = 28,490
22 × 3 × 5 × 13 × 37 = 28,860
2 × 3 × 5 × 7 × 11 × 13 = 30,030
32 × 7 × 13 × 37 = 30,303
3 × 52 × 11 × 37 = 30,525
2 × 3 × 11 × 13 × 37 = 31,746
32 × 52 × 11 × 13 = 32,175
22 × 32 × 52 × 37 = 33,300
2 × 5 × 7 × 13 × 37 = 33,670
22 × 3 × 7 × 11 × 37 = 34,188
2 × 32 × 52 × 7 × 11 = 34,650
22 × 32 × 7 × 11 × 13 = 36,036
3 × 52 × 13 × 37 = 36,075
2 × 32 × 5 × 11 × 37 = 36,630
7 × 11 × 13 × 37 = 37,037
2 × 3 × 52 × 7 × 37 = 38,850
22 × 3 × 7 × 13 × 37 = 40,404
22 × 52 × 11 × 37 = 40,700
2 × 32 × 52 × 7 × 13 = 40,950
3 × 5 × 7 × 11 × 37 = 42,735
22 × 3 × 52 × 11 × 13 = 42,900
2 × 32 × 5 × 13 × 37 = 43,290
32 × 5 × 7 × 11 × 13 = 45,045
22 × 32 × 5 × 7 × 37 = 46,620
32 × 11 × 13 × 37 = 47,619
22 × 52 × 13 × 37 = 48,100
2 × 52 × 7 × 11 × 13 = 50,050
3 × 5 × 7 × 13 × 37 = 50,505
2 × 32 × 7 × 11 × 37 = 51,282
2 × 5 × 11 × 13 × 37 = 52,910
22 × 5 × 7 × 11 × 37 = 56,980
32 × 52 × 7 × 37 = 58,275
22 × 3 × 5 × 7 × 11 × 13 = 60,060
2 × 32 × 7 × 13 × 37 = 60,606
2 × 3 × 52 × 11 × 37 = 61,050
22 × 3 × 11 × 13 × 37 = 63,492
2 × 32 × 52 × 11 × 13 = 64,350
22 × 5 × 7 × 13 × 37 = 67,340
22 × 32 × 52 × 7 × 11 = 69,300
52 × 7 × 11 × 37 = 71,225
2 × 3 × 52 × 13 × 37 = 72,150
22 × 32 × 5 × 11 × 37 = 73,260
2 × 7 × 11 × 13 × 37 = 74,074
3 × 52 × 7 × 11 × 13 = 75,075
22 × 3 × 52 × 7 × 37 = 77,700
3 × 5 × 11 × 13 × 37 = 79,365
22 × 32 × 52 × 7 × 13 = 81,900
52 × 7 × 13 × 37 = 84,175
2 × 3 × 5 × 7 × 11 × 37 = 85,470
22 × 32 × 5 × 13 × 37 = 86,580
2 × 32 × 5 × 7 × 11 × 13 = 90,090
32 × 52 × 11 × 37 = 91,575
2 × 32 × 11 × 13 × 37 = 95,238
22 × 52 × 7 × 11 × 13 = 100,100
2 × 3 × 5 × 7 × 13 × 37 = 101,010
22 × 32 × 7 × 11 × 37 = 102,564
22 × 5 × 11 × 13 × 37 = 105,820
32 × 52 × 13 × 37 = 108,225
3 × 7 × 11 × 13 × 37 = 111,111
2 × 32 × 52 × 7 × 37 = 116,550
22 × 32 × 7 × 13 × 37 = 121,212
22 × 3 × 52 × 11 × 37 = 122,100
32 × 5 × 7 × 11 × 37 = 128,205
22 × 32 × 52 × 11 × 13 = 128,700
52 × 11 × 13 × 37 = 132,275
2 × 52 × 7 × 11 × 37 = 142,450
22 × 3 × 52 × 13 × 37 = 144,300
22 × 7 × 11 × 13 × 37 = 148,148
2 × 3 × 52 × 7 × 11 × 13 = 150,150
32 × 5 × 7 × 13 × 37 = 151,515
2 × 3 × 5 × 11 × 13 × 37 = 158,730
2 × 52 × 7 × 13 × 37 = 168,350
22 × 3 × 5 × 7 × 11 × 37 = 170,940
22 × 32 × 5 × 7 × 11 × 13 = 180,180
2 × 32 × 52 × 11 × 37 = 183,150
5 × 7 × 11 × 13 × 37 = 185,185
22 × 32 × 11 × 13 × 37 = 190,476
22 × 3 × 5 × 7 × 13 × 37 = 202,020
3 × 52 × 7 × 11 × 37 = 213,675
2 × 32 × 52 × 13 × 37 = 216,450
2 × 3 × 7 × 11 × 13 × 37 = 222,222
32 × 52 × 7 × 11 × 13 = 225,225
22 × 32 × 52 × 7 × 37 = 233,100
32 × 5 × 11 × 13 × 37 = 238,095
3 × 52 × 7 × 13 × 37 = 252,525
2 × 32 × 5 × 7 × 11 × 37 = 256,410
2 × 52 × 11 × 13 × 37 = 264,550
22 × 52 × 7 × 11 × 37 = 284,900
22 × 3 × 52 × 7 × 11 × 13 = 300,300
2 × 32 × 5 × 7 × 13 × 37 = 303,030
22 × 3 × 5 × 11 × 13 × 37 = 317,460
32 × 7 × 11 × 13 × 37 = 333,333
22 × 52 × 7 × 13 × 37 = 336,700
22 × 32 × 52 × 11 × 37 = 366,300
2 × 5 × 7 × 11 × 13 × 37 = 370,370
3 × 52 × 11 × 13 × 37 = 396,825
2 × 3 × 52 × 7 × 11 × 37 = 427,350
22 × 32 × 52 × 13 × 37 = 432,900
22 × 3 × 7 × 11 × 13 × 37 = 444,444
2 × 32 × 52 × 7 × 11 × 13 = 450,450
2 × 32 × 5 × 11 × 13 × 37 = 476,190
2 × 3 × 52 × 7 × 13 × 37 = 505,050
22 × 32 × 5 × 7 × 11 × 37 = 512,820
22 × 52 × 11 × 13 × 37 = 529,100
3 × 5 × 7 × 11 × 13 × 37 = 555,555
22 × 32 × 5 × 7 × 13 × 37 = 606,060
32 × 52 × 7 × 11 × 37 = 641,025
2 × 32 × 7 × 11 × 13 × 37 = 666,666
22 × 5 × 7 × 11 × 13 × 37 = 740,740
32 × 52 × 7 × 13 × 37 = 757,575
2 × 3 × 52 × 11 × 13 × 37 = 793,650
22 × 3 × 52 × 7 × 11 × 37 = 854,700
22 × 32 × 52 × 7 × 11 × 13 = 900,900
52 × 7 × 11 × 13 × 37 = 925,925
22 × 32 × 5 × 11 × 13 × 37 = 952,380
22 × 3 × 52 × 7 × 13 × 37 = 1,010,100
2 × 3 × 5 × 7 × 11 × 13 × 37 = 1,111,110
32 × 52 × 11 × 13 × 37 = 1,190,475
2 × 32 × 52 × 7 × 11 × 37 = 1,282,050
22 × 32 × 7 × 11 × 13 × 37 = 1,333,332
2 × 32 × 52 × 7 × 13 × 37 = 1,515,150
22 × 3 × 52 × 11 × 13 × 37 = 1,587,300
32 × 5 × 7 × 11 × 13 × 37 = 1,666,665
2 × 52 × 7 × 11 × 13 × 37 = 1,851,850
22 × 3 × 5 × 7 × 11 × 13 × 37 = 2,222,220
2 × 32 × 52 × 11 × 13 × 37 = 2,380,950
22 × 32 × 52 × 7 × 11 × 37 = 2,564,100
3 × 52 × 7 × 11 × 13 × 37 = 2,777,775
22 × 32 × 52 × 7 × 13 × 37 = 3,030,300
2 × 32 × 5 × 7 × 11 × 13 × 37 = 3,333,330
22 × 52 × 7 × 11 × 13 × 37 = 3,703,700
22 × 32 × 52 × 11 × 13 × 37 = 4,761,900
2 × 3 × 52 × 7 × 11 × 13 × 37 = 5,555,550
22 × 32 × 5 × 7 × 11 × 13 × 37 = 6,666,660
32 × 52 × 7 × 11 × 13 × 37 = 8,333,325
22 × 3 × 52 × 7 × 11 × 13 × 37 = 11,111,100
2 × 32 × 52 × 7 × 11 × 13 × 37 = 16,666,650
22 × 32 × 52 × 7 × 11 × 13 × 37 = 33,333,300

The final answer:
(scroll down)

33,333,300 has 432 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 11; 12; 13; 14; 15; 18; 20; 21; 22; 25; 26; 28; 30; 33; 35; 36; 37; 39; 42; 44; 45; 50; 52; 55; 60; 63; 65; 66; 70; 74; 75; 77; 78; 84; 90; 91; 99; 100; 105; 110; 111; 117; 126; 130; 132; 140; 143; 148; 150; 154; 156; 165; 175; 180; 182; 185; 195; 198; 210; 220; 222; 225; 231; 234; 252; 259; 260; 273; 275; 286; 300; 308; 315; 325; 330; 333; 350; 364; 370; 385; 390; 396; 407; 420; 429; 444; 450; 455; 462; 468; 481; 495; 518; 525; 546; 550; 555; 572; 585; 630; 650; 660; 666; 693; 700; 715; 740; 770; 777; 780; 814; 819; 825; 858; 900; 910; 924; 925; 962; 975; 990; 1,001; 1,036; 1,050; 1,092; 1,100; 1,110; 1,155; 1,170; 1,221; 1,260; 1,287; 1,295; 1,300; 1,332; 1,365; 1,386; 1,430; 1,443; 1,540; 1,554; 1,575; 1,628; 1,638; 1,650; 1,665; 1,716; 1,820; 1,850; 1,924; 1,925; 1,950; 1,980; 2,002; 2,035; 2,100; 2,145; 2,220; 2,275; 2,310; 2,331; 2,340; 2,405; 2,442; 2,475; 2,574; 2,590; 2,730; 2,772; 2,775; 2,849; 2,860; 2,886; 2,925; 3,003; 3,108; 3,150; 3,276; 3,300; 3,330; 3,367; 3,465; 3,575; 3,663; 3,700; 3,850; 3,885; 3,900; 4,004; 4,070; 4,095; 4,290; 4,329; 4,550; 4,620; 4,662; 4,810; 4,884; 4,950; 5,005; 5,148; 5,180; 5,291; 5,460; 5,550; 5,698; 5,772; 5,775; 5,850; 6,006; 6,105; 6,300; 6,435; 6,475; 6,660; 6,734; 6,825; 6,930; 7,150; 7,215; 7,326; 7,700; 7,770; 8,140; 8,190; 8,325; 8,547; 8,580; 8,658; 9,009; 9,100; 9,324; 9,620; 9,900; 10,010; 10,101; 10,175; 10,582; 10,725; 11,100; 11,396; 11,550; 11,655; 11,700; 12,012; 12,025; 12,210; 12,870; 12,950; 13,468; 13,650; 13,860; 14,245; 14,300; 14,430; 14,652; 15,015; 15,540; 15,873; 16,380; 16,650; 16,835; 17,094; 17,316; 17,325; 18,018; 18,315; 19,425; 20,020; 20,202; 20,350; 20,475; 21,164; 21,450; 21,645; 23,100; 23,310; 24,050; 24,420; 25,025; 25,641; 25,740; 25,900; 26,455; 27,300; 28,490; 28,860; 30,030; 30,303; 30,525; 31,746; 32,175; 33,300; 33,670; 34,188; 34,650; 36,036; 36,075; 36,630; 37,037; 38,850; 40,404; 40,700; 40,950; 42,735; 42,900; 43,290; 45,045; 46,620; 47,619; 48,100; 50,050; 50,505; 51,282; 52,910; 56,980; 58,275; 60,060; 60,606; 61,050; 63,492; 64,350; 67,340; 69,300; 71,225; 72,150; 73,260; 74,074; 75,075; 77,700; 79,365; 81,900; 84,175; 85,470; 86,580; 90,090; 91,575; 95,238; 100,100; 101,010; 102,564; 105,820; 108,225; 111,111; 116,550; 121,212; 122,100; 128,205; 128,700; 132,275; 142,450; 144,300; 148,148; 150,150; 151,515; 158,730; 168,350; 170,940; 180,180; 183,150; 185,185; 190,476; 202,020; 213,675; 216,450; 222,222; 225,225; 233,100; 238,095; 252,525; 256,410; 264,550; 284,900; 300,300; 303,030; 317,460; 333,333; 336,700; 366,300; 370,370; 396,825; 427,350; 432,900; 444,444; 450,450; 476,190; 505,050; 512,820; 529,100; 555,555; 606,060; 641,025; 666,666; 740,740; 757,575; 793,650; 854,700; 900,900; 925,925; 952,380; 1,010,100; 1,111,110; 1,190,475; 1,282,050; 1,333,332; 1,515,150; 1,587,300; 1,666,665; 1,851,850; 2,222,220; 2,380,950; 2,564,100; 2,777,775; 3,030,300; 3,333,330; 3,703,700; 4,761,900; 5,555,550; 6,666,660; 8,333,325; 11,111,100; 16,666,650 and 33,333,300
out of which 7 prime factors: 2; 3; 5; 7; 11; 13 and 37
33,333,300 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.


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".