Calculate All the Factors of 56,628,000

All the factors (divisors) of the number 56,628,000. How important is the prime factorization of the number

1. Carry out the prime factorization of the number 56,628,000:

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

56,628,000 = 25 × 32 × 53 × 112 × 13
56,628,000 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 = (5 + 1) × (2 + 1) × (3 + 1) × (2 + 1) × (1 + 1) = 6 × 3 × 4 × 3 × 2 = 432

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

2. Multiply the prime factors of the number 56,628,000

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
23 = 8
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
prime factor = 13
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
2 × 11 = 22
23 × 3 = 24
52 = 25
2 × 13 = 26
2 × 3 × 5 = 30
25 = 32
3 × 11 = 33
22 × 32 = 36
3 × 13 = 39
23 × 5 = 40
22 × 11 = 44
32 × 5 = 45
24 × 3 = 48
2 × 52 = 50
22 × 13 = 52
5 × 11 = 55
22 × 3 × 5 = 60
5 × 13 = 65
2 × 3 × 11 = 66
23 × 32 = 72
3 × 52 = 75
2 × 3 × 13 = 78
24 × 5 = 80
23 × 11 = 88
2 × 32 × 5 = 90
25 × 3 = 96
32 × 11 = 99
22 × 52 = 100
23 × 13 = 104
2 × 5 × 11 = 110
32 × 13 = 117
23 × 3 × 5 = 120
112 = 121
53 = 125
2 × 5 × 13 = 130
22 × 3 × 11 = 132
11 × 13 = 143
24 × 32 = 144
2 × 3 × 52 = 150
22 × 3 × 13 = 156
25 × 5 = 160
3 × 5 × 11 = 165
24 × 11 = 176
22 × 32 × 5 = 180
3 × 5 × 13 = 195
2 × 32 × 11 = 198
23 × 52 = 200
24 × 13 = 208
22 × 5 × 11 = 220
32 × 52 = 225
2 × 32 × 13 = 234
24 × 3 × 5 = 240
2 × 112 = 242
2 × 53 = 250
22 × 5 × 13 = 260
23 × 3 × 11 = 264
52 × 11 = 275
2 × 11 × 13 = 286
25 × 32 = 288
22 × 3 × 52 = 300
23 × 3 × 13 = 312
52 × 13 = 325
2 × 3 × 5 × 11 = 330
25 × 11 = 352
23 × 32 × 5 = 360
3 × 112 = 363
3 × 53 = 375
2 × 3 × 5 × 13 = 390
22 × 32 × 11 = 396
24 × 52 = 400
25 × 13 = 416
3 × 11 × 13 = 429
23 × 5 × 11 = 440
2 × 32 × 52 = 450
22 × 32 × 13 = 468
25 × 3 × 5 = 480
22 × 112 = 484
32 × 5 × 11 = 495
22 × 53 = 500
23 × 5 × 13 = 520
24 × 3 × 11 = 528
2 × 52 × 11 = 550
22 × 11 × 13 = 572
32 × 5 × 13 = 585
23 × 3 × 52 = 600
5 × 112 = 605
24 × 3 × 13 = 624
2 × 52 × 13 = 650
22 × 3 × 5 × 11 = 660
5 × 11 × 13 = 715
24 × 32 × 5 = 720
2 × 3 × 112 = 726
2 × 3 × 53 = 750
22 × 3 × 5 × 13 = 780
23 × 32 × 11 = 792
25 × 52 = 800
3 × 52 × 11 = 825
2 × 3 × 11 × 13 = 858
24 × 5 × 11 = 880
22 × 32 × 52 = 900
23 × 32 × 13 = 936
23 × 112 = 968
3 × 52 × 13 = 975
2 × 32 × 5 × 11 = 990
23 × 53 = 1,000
24 × 5 × 13 = 1,040
25 × 3 × 11 = 1,056
32 × 112 = 1,089
22 × 52 × 11 = 1,100
32 × 53 = 1,125
23 × 11 × 13 = 1,144
2 × 32 × 5 × 13 = 1,170
24 × 3 × 52 = 1,200
2 × 5 × 112 = 1,210
25 × 3 × 13 = 1,248
32 × 11 × 13 = 1,287
22 × 52 × 13 = 1,300
23 × 3 × 5 × 11 = 1,320
53 × 11 = 1,375
2 × 5 × 11 × 13 = 1,430
25 × 32 × 5 = 1,440
22 × 3 × 112 = 1,452
22 × 3 × 53 = 1,500
23 × 3 × 5 × 13 = 1,560
112 × 13 = 1,573
24 × 32 × 11 = 1,584
53 × 13 = 1,625
2 × 3 × 52 × 11 = 1,650
22 × 3 × 11 × 13 = 1,716
25 × 5 × 11 = 1,760
23 × 32 × 52 = 1,800
3 × 5 × 112 = 1,815
24 × 32 × 13 = 1,872
24 × 112 = 1,936
2 × 3 × 52 × 13 = 1,950
22 × 32 × 5 × 11 = 1,980
24 × 53 = 2,000
25 × 5 × 13 = 2,080
3 × 5 × 11 × 13 = 2,145
2 × 32 × 112 = 2,178
23 × 52 × 11 = 2,200
2 × 32 × 53 = 2,250
24 × 11 × 13 = 2,288
22 × 32 × 5 × 13 = 2,340
25 × 3 × 52 = 2,400
22 × 5 × 112 = 2,420
32 × 52 × 11 = 2,475
2 × 32 × 11 × 13 = 2,574
23 × 52 × 13 = 2,600
24 × 3 × 5 × 11 = 2,640
2 × 53 × 11 = 2,750
22 × 5 × 11 × 13 = 2,860
23 × 3 × 112 = 2,904
32 × 52 × 13 = 2,925
23 × 3 × 53 = 3,000
52 × 112 = 3,025
24 × 3 × 5 × 13 = 3,120
2 × 112 × 13 = 3,146
25 × 32 × 11 = 3,168
2 × 53 × 13 = 3,250
22 × 3 × 52 × 11 = 3,300
23 × 3 × 11 × 13 = 3,432
52 × 11 × 13 = 3,575
24 × 32 × 52 = 3,600
2 × 3 × 5 × 112 = 3,630
25 × 32 × 13 = 3,744
25 × 112 = 3,872
22 × 3 × 52 × 13 = 3,900
23 × 32 × 5 × 11 = 3,960
25 × 53 = 4,000
3 × 53 × 11 = 4,125
2 × 3 × 5 × 11 × 13 = 4,290
22 × 32 × 112 = 4,356
24 × 52 × 11 = 4,400
22 × 32 × 53 = 4,500
25 × 11 × 13 = 4,576
23 × 32 × 5 × 13 = 4,680
3 × 112 × 13 = 4,719
23 × 5 × 112 = 4,840
3 × 53 × 13 = 4,875
2 × 32 × 52 × 11 = 4,950
22 × 32 × 11 × 13 = 5,148
24 × 52 × 13 = 5,200
25 × 3 × 5 × 11 = 5,280
32 × 5 × 112 = 5,445
22 × 53 × 11 = 5,500
23 × 5 × 11 × 13 = 5,720
24 × 3 × 112 = 5,808
2 × 32 × 52 × 13 = 5,850
24 × 3 × 53 = 6,000
2 × 52 × 112 = 6,050
25 × 3 × 5 × 13 = 6,240
22 × 112 × 13 = 6,292
32 × 5 × 11 × 13 = 6,435
22 × 53 × 13 = 6,500
23 × 3 × 52 × 11 = 6,600
24 × 3 × 11 × 13 = 6,864
2 × 52 × 11 × 13 = 7,150
25 × 32 × 52 = 7,200
22 × 3 × 5 × 112 = 7,260
This list continues below...

... This list continues from above
23 × 3 × 52 × 13 = 7,800
5 × 112 × 13 = 7,865
24 × 32 × 5 × 11 = 7,920
2 × 3 × 53 × 11 = 8,250
22 × 3 × 5 × 11 × 13 = 8,580
23 × 32 × 112 = 8,712
25 × 52 × 11 = 8,800
23 × 32 × 53 = 9,000
3 × 52 × 112 = 9,075
24 × 32 × 5 × 13 = 9,360
2 × 3 × 112 × 13 = 9,438
24 × 5 × 112 = 9,680
2 × 3 × 53 × 13 = 9,750
22 × 32 × 52 × 11 = 9,900
23 × 32 × 11 × 13 = 10,296
25 × 52 × 13 = 10,400
3 × 52 × 11 × 13 = 10,725
2 × 32 × 5 × 112 = 10,890
23 × 53 × 11 = 11,000
24 × 5 × 11 × 13 = 11,440
25 × 3 × 112 = 11,616
22 × 32 × 52 × 13 = 11,700
25 × 3 × 53 = 12,000
22 × 52 × 112 = 12,100
32 × 53 × 11 = 12,375
23 × 112 × 13 = 12,584
2 × 32 × 5 × 11 × 13 = 12,870
23 × 53 × 13 = 13,000
24 × 3 × 52 × 11 = 13,200
25 × 3 × 11 × 13 = 13,728
32 × 112 × 13 = 14,157
22 × 52 × 11 × 13 = 14,300
23 × 3 × 5 × 112 = 14,520
32 × 53 × 13 = 14,625
53 × 112 = 15,125
24 × 3 × 52 × 13 = 15,600
2 × 5 × 112 × 13 = 15,730
25 × 32 × 5 × 11 = 15,840
22 × 3 × 53 × 11 = 16,500
23 × 3 × 5 × 11 × 13 = 17,160
24 × 32 × 112 = 17,424
53 × 11 × 13 = 17,875
24 × 32 × 53 = 18,000
2 × 3 × 52 × 112 = 18,150
25 × 32 × 5 × 13 = 18,720
22 × 3 × 112 × 13 = 18,876
25 × 5 × 112 = 19,360
22 × 3 × 53 × 13 = 19,500
23 × 32 × 52 × 11 = 19,800
24 × 32 × 11 × 13 = 20,592
2 × 3 × 52 × 11 × 13 = 21,450
22 × 32 × 5 × 112 = 21,780
24 × 53 × 11 = 22,000
25 × 5 × 11 × 13 = 22,880
23 × 32 × 52 × 13 = 23,400
3 × 5 × 112 × 13 = 23,595
23 × 52 × 112 = 24,200
2 × 32 × 53 × 11 = 24,750
24 × 112 × 13 = 25,168
22 × 32 × 5 × 11 × 13 = 25,740
24 × 53 × 13 = 26,000
25 × 3 × 52 × 11 = 26,400
32 × 52 × 112 = 27,225
2 × 32 × 112 × 13 = 28,314
23 × 52 × 11 × 13 = 28,600
24 × 3 × 5 × 112 = 29,040
2 × 32 × 53 × 13 = 29,250
2 × 53 × 112 = 30,250
25 × 3 × 52 × 13 = 31,200
22 × 5 × 112 × 13 = 31,460
32 × 52 × 11 × 13 = 32,175
23 × 3 × 53 × 11 = 33,000
24 × 3 × 5 × 11 × 13 = 34,320
25 × 32 × 112 = 34,848
2 × 53 × 11 × 13 = 35,750
25 × 32 × 53 = 36,000
22 × 3 × 52 × 112 = 36,300
23 × 3 × 112 × 13 = 37,752
23 × 3 × 53 × 13 = 39,000
52 × 112 × 13 = 39,325
24 × 32 × 52 × 11 = 39,600
25 × 32 × 11 × 13 = 41,184
22 × 3 × 52 × 11 × 13 = 42,900
23 × 32 × 5 × 112 = 43,560
25 × 53 × 11 = 44,000
3 × 53 × 112 = 45,375
24 × 32 × 52 × 13 = 46,800
2 × 3 × 5 × 112 × 13 = 47,190
24 × 52 × 112 = 48,400
22 × 32 × 53 × 11 = 49,500
25 × 112 × 13 = 50,336
23 × 32 × 5 × 11 × 13 = 51,480
25 × 53 × 13 = 52,000
3 × 53 × 11 × 13 = 53,625
2 × 32 × 52 × 112 = 54,450
22 × 32 × 112 × 13 = 56,628
24 × 52 × 11 × 13 = 57,200
25 × 3 × 5 × 112 = 58,080
22 × 32 × 53 × 13 = 58,500
22 × 53 × 112 = 60,500
23 × 5 × 112 × 13 = 62,920
2 × 32 × 52 × 11 × 13 = 64,350
24 × 3 × 53 × 11 = 66,000
25 × 3 × 5 × 11 × 13 = 68,640
32 × 5 × 112 × 13 = 70,785
22 × 53 × 11 × 13 = 71,500
23 × 3 × 52 × 112 = 72,600
24 × 3 × 112 × 13 = 75,504
24 × 3 × 53 × 13 = 78,000
2 × 52 × 112 × 13 = 78,650
25 × 32 × 52 × 11 = 79,200
23 × 3 × 52 × 11 × 13 = 85,800
24 × 32 × 5 × 112 = 87,120
2 × 3 × 53 × 112 = 90,750
25 × 32 × 52 × 13 = 93,600
22 × 3 × 5 × 112 × 13 = 94,380
25 × 52 × 112 = 96,800
23 × 32 × 53 × 11 = 99,000
24 × 32 × 5 × 11 × 13 = 102,960
2 × 3 × 53 × 11 × 13 = 107,250
22 × 32 × 52 × 112 = 108,900
23 × 32 × 112 × 13 = 113,256
25 × 52 × 11 × 13 = 114,400
23 × 32 × 53 × 13 = 117,000
3 × 52 × 112 × 13 = 117,975
23 × 53 × 112 = 121,000
24 × 5 × 112 × 13 = 125,840
22 × 32 × 52 × 11 × 13 = 128,700
25 × 3 × 53 × 11 = 132,000
32 × 53 × 112 = 136,125
2 × 32 × 5 × 112 × 13 = 141,570
23 × 53 × 11 × 13 = 143,000
24 × 3 × 52 × 112 = 145,200
25 × 3 × 112 × 13 = 151,008
25 × 3 × 53 × 13 = 156,000
22 × 52 × 112 × 13 = 157,300
32 × 53 × 11 × 13 = 160,875
24 × 3 × 52 × 11 × 13 = 171,600
25 × 32 × 5 × 112 = 174,240
22 × 3 × 53 × 112 = 181,500
23 × 3 × 5 × 112 × 13 = 188,760
53 × 112 × 13 = 196,625
24 × 32 × 53 × 11 = 198,000
25 × 32 × 5 × 11 × 13 = 205,920
22 × 3 × 53 × 11 × 13 = 214,500
23 × 32 × 52 × 112 = 217,800
24 × 32 × 112 × 13 = 226,512
24 × 32 × 53 × 13 = 234,000
2 × 3 × 52 × 112 × 13 = 235,950
24 × 53 × 112 = 242,000
25 × 5 × 112 × 13 = 251,680
23 × 32 × 52 × 11 × 13 = 257,400
2 × 32 × 53 × 112 = 272,250
22 × 32 × 5 × 112 × 13 = 283,140
24 × 53 × 11 × 13 = 286,000
25 × 3 × 52 × 112 = 290,400
23 × 52 × 112 × 13 = 314,600
2 × 32 × 53 × 11 × 13 = 321,750
25 × 3 × 52 × 11 × 13 = 343,200
32 × 52 × 112 × 13 = 353,925
23 × 3 × 53 × 112 = 363,000
24 × 3 × 5 × 112 × 13 = 377,520
2 × 53 × 112 × 13 = 393,250
25 × 32 × 53 × 11 = 396,000
23 × 3 × 53 × 11 × 13 = 429,000
24 × 32 × 52 × 112 = 435,600
25 × 32 × 112 × 13 = 453,024
25 × 32 × 53 × 13 = 468,000
22 × 3 × 52 × 112 × 13 = 471,900
25 × 53 × 112 = 484,000
24 × 32 × 52 × 11 × 13 = 514,800
22 × 32 × 53 × 112 = 544,500
23 × 32 × 5 × 112 × 13 = 566,280
25 × 53 × 11 × 13 = 572,000
3 × 53 × 112 × 13 = 589,875
24 × 52 × 112 × 13 = 629,200
22 × 32 × 53 × 11 × 13 = 643,500
2 × 32 × 52 × 112 × 13 = 707,850
24 × 3 × 53 × 112 = 726,000
25 × 3 × 5 × 112 × 13 = 755,040
22 × 53 × 112 × 13 = 786,500
24 × 3 × 53 × 11 × 13 = 858,000
25 × 32 × 52 × 112 = 871,200
23 × 3 × 52 × 112 × 13 = 943,800
25 × 32 × 52 × 11 × 13 = 1,029,600
23 × 32 × 53 × 112 = 1,089,000
24 × 32 × 5 × 112 × 13 = 1,132,560
2 × 3 × 53 × 112 × 13 = 1,179,750
25 × 52 × 112 × 13 = 1,258,400
23 × 32 × 53 × 11 × 13 = 1,287,000
22 × 32 × 52 × 112 × 13 = 1,415,700
25 × 3 × 53 × 112 = 1,452,000
23 × 53 × 112 × 13 = 1,573,000
25 × 3 × 53 × 11 × 13 = 1,716,000
32 × 53 × 112 × 13 = 1,769,625
24 × 3 × 52 × 112 × 13 = 1,887,600
24 × 32 × 53 × 112 = 2,178,000
25 × 32 × 5 × 112 × 13 = 2,265,120
22 × 3 × 53 × 112 × 13 = 2,359,500
24 × 32 × 53 × 11 × 13 = 2,574,000
23 × 32 × 52 × 112 × 13 = 2,831,400
24 × 53 × 112 × 13 = 3,146,000
2 × 32 × 53 × 112 × 13 = 3,539,250
25 × 3 × 52 × 112 × 13 = 3,775,200
25 × 32 × 53 × 112 = 4,356,000
23 × 3 × 53 × 112 × 13 = 4,719,000
25 × 32 × 53 × 11 × 13 = 5,148,000
24 × 32 × 52 × 112 × 13 = 5,662,800
25 × 53 × 112 × 13 = 6,292,000
22 × 32 × 53 × 112 × 13 = 7,078,500
24 × 3 × 53 × 112 × 13 = 9,438,000
25 × 32 × 52 × 112 × 13 = 11,325,600
23 × 32 × 53 × 112 × 13 = 14,157,000
25 × 3 × 53 × 112 × 13 = 18,876,000
24 × 32 × 53 × 112 × 13 = 28,314,000
25 × 32 × 53 × 112 × 13 = 56,628,000

The final answer:
(scroll down)

56,628,000 has 432 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 11; 12; 13; 15; 16; 18; 20; 22; 24; 25; 26; 30; 32; 33; 36; 39; 40; 44; 45; 48; 50; 52; 55; 60; 65; 66; 72; 75; 78; 80; 88; 90; 96; 99; 100; 104; 110; 117; 120; 121; 125; 130; 132; 143; 144; 150; 156; 160; 165; 176; 180; 195; 198; 200; 208; 220; 225; 234; 240; 242; 250; 260; 264; 275; 286; 288; 300; 312; 325; 330; 352; 360; 363; 375; 390; 396; 400; 416; 429; 440; 450; 468; 480; 484; 495; 500; 520; 528; 550; 572; 585; 600; 605; 624; 650; 660; 715; 720; 726; 750; 780; 792; 800; 825; 858; 880; 900; 936; 968; 975; 990; 1,000; 1,040; 1,056; 1,089; 1,100; 1,125; 1,144; 1,170; 1,200; 1,210; 1,248; 1,287; 1,300; 1,320; 1,375; 1,430; 1,440; 1,452; 1,500; 1,560; 1,573; 1,584; 1,625; 1,650; 1,716; 1,760; 1,800; 1,815; 1,872; 1,936; 1,950; 1,980; 2,000; 2,080; 2,145; 2,178; 2,200; 2,250; 2,288; 2,340; 2,400; 2,420; 2,475; 2,574; 2,600; 2,640; 2,750; 2,860; 2,904; 2,925; 3,000; 3,025; 3,120; 3,146; 3,168; 3,250; 3,300; 3,432; 3,575; 3,600; 3,630; 3,744; 3,872; 3,900; 3,960; 4,000; 4,125; 4,290; 4,356; 4,400; 4,500; 4,576; 4,680; 4,719; 4,840; 4,875; 4,950; 5,148; 5,200; 5,280; 5,445; 5,500; 5,720; 5,808; 5,850; 6,000; 6,050; 6,240; 6,292; 6,435; 6,500; 6,600; 6,864; 7,150; 7,200; 7,260; 7,800; 7,865; 7,920; 8,250; 8,580; 8,712; 8,800; 9,000; 9,075; 9,360; 9,438; 9,680; 9,750; 9,900; 10,296; 10,400; 10,725; 10,890; 11,000; 11,440; 11,616; 11,700; 12,000; 12,100; 12,375; 12,584; 12,870; 13,000; 13,200; 13,728; 14,157; 14,300; 14,520; 14,625; 15,125; 15,600; 15,730; 15,840; 16,500; 17,160; 17,424; 17,875; 18,000; 18,150; 18,720; 18,876; 19,360; 19,500; 19,800; 20,592; 21,450; 21,780; 22,000; 22,880; 23,400; 23,595; 24,200; 24,750; 25,168; 25,740; 26,000; 26,400; 27,225; 28,314; 28,600; 29,040; 29,250; 30,250; 31,200; 31,460; 32,175; 33,000; 34,320; 34,848; 35,750; 36,000; 36,300; 37,752; 39,000; 39,325; 39,600; 41,184; 42,900; 43,560; 44,000; 45,375; 46,800; 47,190; 48,400; 49,500; 50,336; 51,480; 52,000; 53,625; 54,450; 56,628; 57,200; 58,080; 58,500; 60,500; 62,920; 64,350; 66,000; 68,640; 70,785; 71,500; 72,600; 75,504; 78,000; 78,650; 79,200; 85,800; 87,120; 90,750; 93,600; 94,380; 96,800; 99,000; 102,960; 107,250; 108,900; 113,256; 114,400; 117,000; 117,975; 121,000; 125,840; 128,700; 132,000; 136,125; 141,570; 143,000; 145,200; 151,008; 156,000; 157,300; 160,875; 171,600; 174,240; 181,500; 188,760; 196,625; 198,000; 205,920; 214,500; 217,800; 226,512; 234,000; 235,950; 242,000; 251,680; 257,400; 272,250; 283,140; 286,000; 290,400; 314,600; 321,750; 343,200; 353,925; 363,000; 377,520; 393,250; 396,000; 429,000; 435,600; 453,024; 468,000; 471,900; 484,000; 514,800; 544,500; 566,280; 572,000; 589,875; 629,200; 643,500; 707,850; 726,000; 755,040; 786,500; 858,000; 871,200; 943,800; 1,029,600; 1,089,000; 1,132,560; 1,179,750; 1,258,400; 1,287,000; 1,415,700; 1,452,000; 1,573,000; 1,716,000; 1,769,625; 1,887,600; 2,178,000; 2,265,120; 2,359,500; 2,574,000; 2,831,400; 3,146,000; 3,539,250; 3,775,200; 4,356,000; 4,719,000; 5,148,000; 5,662,800; 6,292,000; 7,078,500; 9,438,000; 11,325,600; 14,157,000; 18,876,000; 28,314,000 and 56,628,000
out of which 5 prime factors: 2; 3; 5; 11 and 13
56,628,000 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:

» What are all the proper, improper and prime factors (divisors) of the number 56,627,999?

» New: All the Calculations Performed by Our Visitors: Common Divisors of Numbers. Data organized on a Monthly Basis

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".