1,828,170,000 and 2,193,804,000: All the common factors (divisors) and prime factors of the integer numbers

The common factors of numbers 1,828,170,000 and 2,193,804,000

The common factors (divisors) of numbers 1,828,170,000 and 2,193,804,000 are all the factors (divisors) of their 'greatest (highest) common factor (divisor)'.

Note

Factor of a number A: a number B that when multiplied with another C produces the given number A. Both B and C are factors of A.



Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd. Follow the two steps below.

Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


1,828,170,000 = 24 × 34 × 54 × 37 × 61;
1,828,170,000 is not a prime, is a composite number;


2,193,804,000 = 25 × 35 × 53 × 37 × 61;
2,193,804,000 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.




Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd

Multiply all the common prime factors, by the lowest exponents (if any).


Greatest (highest) common factor (divisor):


gcf, hcf, gcd (1,828,170,000; 2,193,804,000) = 24 × 34 × 53 × 37 × 61 = 365,634,000;




Find all the factors (divisors) of the GCF (HCF, GCD)

365,634,000 = 24 × 34 × 53 × 37 × 61


Get all the combinations (multiplications) of the prime factors of GFC (HCF, GCD) that give different results.


When combining the prime factors also consider their exponents.


Also add 1 to the list of factors (divisors). Any number is divisible by 1.


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



Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
continued below...
... continued from above
2 × 32 = 18
22 × 5 = 20
23 × 3 = 24
52 = 25
33 = 27
2 × 3 × 5 = 30
22 × 32 = 36
prime factor = 37
23 × 5 = 40
32 × 5 = 45
24 × 3 = 48
2 × 52 = 50
2 × 33 = 54
22 × 3 × 5 = 60
prime factor = 61
23 × 32 = 72
2 × 37 = 74
3 × 52 = 75
24 × 5 = 80
34 = 81
2 × 32 × 5 = 90
22 × 52 = 100
22 × 33 = 108
3 × 37 = 111
23 × 3 × 5 = 120
2 × 61 = 122
53 = 125
33 × 5 = 135
24 × 32 = 144
22 × 37 = 148
2 × 3 × 52 = 150
2 × 34 = 162
22 × 32 × 5 = 180
3 × 61 = 183
5 × 37 = 185
23 × 52 = 200
23 × 33 = 216
2 × 3 × 37 = 222
32 × 52 = 225
24 × 3 × 5 = 240
22 × 61 = 244
2 × 53 = 250
2 × 33 × 5 = 270
23 × 37 = 296
22 × 3 × 52 = 300
5 × 61 = 305
22 × 34 = 324
32 × 37 = 333
23 × 32 × 5 = 360
2 × 3 × 61 = 366
2 × 5 × 37 = 370
3 × 53 = 375
24 × 52 = 400
34 × 5 = 405
24 × 33 = 432
22 × 3 × 37 = 444
2 × 32 × 52 = 450
23 × 61 = 488
22 × 53 = 500
22 × 33 × 5 = 540
32 × 61 = 549
3 × 5 × 37 = 555
24 × 37 = 592
23 × 3 × 52 = 600
2 × 5 × 61 = 610
23 × 34 = 648
2 × 32 × 37 = 666
33 × 52 = 675
24 × 32 × 5 = 720
22 × 3 × 61 = 732
22 × 5 × 37 = 740
2 × 3 × 53 = 750
2 × 34 × 5 = 810
23 × 3 × 37 = 888
22 × 32 × 52 = 900
3 × 5 × 61 = 915
52 × 37 = 925
24 × 61 = 976
33 × 37 = 999
23 × 53 = 1,000
23 × 33 × 5 = 1,080
2 × 32 × 61 = 1,098
2 × 3 × 5 × 37 = 1,110
32 × 53 = 1,125
24 × 3 × 52 = 1,200
22 × 5 × 61 = 1,220
24 × 34 = 1,296
22 × 32 × 37 = 1,332
2 × 33 × 52 = 1,350
23 × 3 × 61 = 1,464
23 × 5 × 37 = 1,480
22 × 3 × 53 = 1,500
52 × 61 = 1,525
22 × 34 × 5 = 1,620
33 × 61 = 1,647
32 × 5 × 37 = 1,665
24 × 3 × 37 = 1,776
23 × 32 × 52 = 1,800
2 × 3 × 5 × 61 = 1,830
2 × 52 × 37 = 1,850
2 × 33 × 37 = 1,998
24 × 53 = 2,000
34 × 52 = 2,025
24 × 33 × 5 = 2,160
22 × 32 × 61 = 2,196
22 × 3 × 5 × 37 = 2,220
2 × 32 × 53 = 2,250
37 × 61 = 2,257
23 × 5 × 61 = 2,440
23 × 32 × 37 = 2,664
22 × 33 × 52 = 2,700
32 × 5 × 61 = 2,745
3 × 52 × 37 = 2,775
24 × 3 × 61 = 2,928
24 × 5 × 37 = 2,960
34 × 37 = 2,997
23 × 3 × 53 = 3,000
2 × 52 × 61 = 3,050
23 × 34 × 5 = 3,240
2 × 33 × 61 = 3,294
2 × 32 × 5 × 37 = 3,330
33 × 53 = 3,375
24 × 32 × 52 = 3,600
22 × 3 × 5 × 61 = 3,660
22 × 52 × 37 = 3,700
22 × 33 × 37 = 3,996
2 × 34 × 52 = 4,050
23 × 32 × 61 = 4,392
23 × 3 × 5 × 37 = 4,440
22 × 32 × 53 = 4,500
2 × 37 × 61 = 4,514
3 × 52 × 61 = 4,575
53 × 37 = 4,625
24 × 5 × 61 = 4,880
34 × 61 = 4,941
33 × 5 × 37 = 4,995
24 × 32 × 37 = 5,328
23 × 33 × 52 = 5,400
2 × 32 × 5 × 61 = 5,490
2 × 3 × 52 × 37 = 5,550
2 × 34 × 37 = 5,994
24 × 3 × 53 = 6,000
22 × 52 × 61 = 6,100
24 × 34 × 5 = 6,480
22 × 33 × 61 = 6,588
22 × 32 × 5 × 37 = 6,660
2 × 33 × 53 = 6,750
3 × 37 × 61 = 6,771
23 × 3 × 5 × 61 = 7,320
23 × 52 × 37 = 7,400
53 × 61 = 7,625
23 × 33 × 37 = 7,992
22 × 34 × 52 = 8,100
33 × 5 × 61 = 8,235
32 × 52 × 37 = 8,325
24 × 32 × 61 = 8,784
24 × 3 × 5 × 37 = 8,880
23 × 32 × 53 = 9,000
22 × 37 × 61 = 9,028
2 × 3 × 52 × 61 = 9,150
2 × 53 × 37 = 9,250
2 × 34 × 61 = 9,882
2 × 33 × 5 × 37 = 9,990
34 × 53 = 10,125
24 × 33 × 52 = 10,800
22 × 32 × 5 × 61 = 10,980
22 × 3 × 52 × 37 = 11,100
5 × 37 × 61 = 11,285
22 × 34 × 37 = 11,988
23 × 52 × 61 = 12,200
23 × 33 × 61 = 13,176
23 × 32 × 5 × 37 = 13,320
22 × 33 × 53 = 13,500
2 × 3 × 37 × 61 = 13,542
32 × 52 × 61 = 13,725
3 × 53 × 37 = 13,875
24 × 3 × 5 × 61 = 14,640
24 × 52 × 37 = 14,800
34 × 5 × 37 = 14,985
2 × 53 × 61 = 15,250
24 × 33 × 37 = 15,984
23 × 34 × 52 = 16,200
2 × 33 × 5 × 61 = 16,470
2 × 32 × 52 × 37 = 16,650
24 × 32 × 53 = 18,000
23 × 37 × 61 = 18,056
22 × 3 × 52 × 61 = 18,300
22 × 53 × 37 = 18,500
22 × 34 × 61 = 19,764
22 × 33 × 5 × 37 = 19,980
2 × 34 × 53 = 20,250
32 × 37 × 61 = 20,313
23 × 32 × 5 × 61 = 21,960
23 × 3 × 52 × 37 = 22,200
2 × 5 × 37 × 61 = 22,570
3 × 53 × 61 = 22,875
23 × 34 × 37 = 23,976
24 × 52 × 61 = 24,400
34 × 5 × 61 = 24,705
33 × 52 × 37 = 24,975
24 × 33 × 61 = 26,352
24 × 32 × 5 × 37 = 26,640
23 × 33 × 53 = 27,000
22 × 3 × 37 × 61 = 27,084
2 × 32 × 52 × 61 = 27,450
2 × 3 × 53 × 37 = 27,750
2 × 34 × 5 × 37 = 29,970
22 × 53 × 61 = 30,500
24 × 34 × 52 = 32,400
22 × 33 × 5 × 61 = 32,940
22 × 32 × 52 × 37 = 33,300
3 × 5 × 37 × 61 = 33,855
24 × 37 × 61 = 36,112
23 × 3 × 52 × 61 = 36,600
23 × 53 × 37 = 37,000
23 × 34 × 61 = 39,528
23 × 33 × 5 × 37 = 39,960
22 × 34 × 53 = 40,500
2 × 32 × 37 × 61 = 40,626
33 × 52 × 61 = 41,175
32 × 53 × 37 = 41,625
24 × 32 × 5 × 61 = 43,920
24 × 3 × 52 × 37 = 44,400
22 × 5 × 37 × 61 = 45,140
2 × 3 × 53 × 61 = 45,750
24 × 34 × 37 = 47,952
2 × 34 × 5 × 61 = 49,410
2 × 33 × 52 × 37 = 49,950
24 × 33 × 53 = 54,000
23 × 3 × 37 × 61 = 54,168
22 × 32 × 52 × 61 = 54,900
22 × 3 × 53 × 37 = 55,500
52 × 37 × 61 = 56,425
22 × 34 × 5 × 37 = 59,940
33 × 37 × 61 = 60,939
23 × 53 × 61 = 61,000
23 × 33 × 5 × 61 = 65,880
23 × 32 × 52 × 37 = 66,600
2 × 3 × 5 × 37 × 61 = 67,710
32 × 53 × 61 = 68,625
24 × 3 × 52 × 61 = 73,200
24 × 53 × 37 = 74,000
34 × 52 × 37 = 74,925
24 × 34 × 61 = 79,056
24 × 33 × 5 × 37 = 79,920
23 × 34 × 53 = 81,000
22 × 32 × 37 × 61 = 81,252
2 × 33 × 52 × 61 = 82,350
2 × 32 × 53 × 37 = 83,250
23 × 5 × 37 × 61 = 90,280
22 × 3 × 53 × 61 = 91,500
22 × 34 × 5 × 61 = 98,820
22 × 33 × 52 × 37 = 99,900
32 × 5 × 37 × 61 = 101,565
24 × 3 × 37 × 61 = 108,336
23 × 32 × 52 × 61 = 109,800
23 × 3 × 53 × 37 = 111,000
2 × 52 × 37 × 61 = 112,850
23 × 34 × 5 × 37 = 119,880
2 × 33 × 37 × 61 = 121,878
24 × 53 × 61 = 122,000
34 × 52 × 61 = 123,525
33 × 53 × 37 = 124,875
24 × 33 × 5 × 61 = 131,760
24 × 32 × 52 × 37 = 133,200
22 × 3 × 5 × 37 × 61 = 135,420
2 × 32 × 53 × 61 = 137,250
2 × 34 × 52 × 37 = 149,850
24 × 34 × 53 = 162,000
23 × 32 × 37 × 61 = 162,504
22 × 33 × 52 × 61 = 164,700
22 × 32 × 53 × 37 = 166,500
3 × 52 × 37 × 61 = 169,275
24 × 5 × 37 × 61 = 180,560
34 × 37 × 61 = 182,817
23 × 3 × 53 × 61 = 183,000
23 × 34 × 5 × 61 = 197,640
23 × 33 × 52 × 37 = 199,800
2 × 32 × 5 × 37 × 61 = 203,130
33 × 53 × 61 = 205,875
24 × 32 × 52 × 61 = 219,600
24 × 3 × 53 × 37 = 222,000
22 × 52 × 37 × 61 = 225,700
24 × 34 × 5 × 37 = 239,760
22 × 33 × 37 × 61 = 243,756
2 × 34 × 52 × 61 = 247,050
2 × 33 × 53 × 37 = 249,750
23 × 3 × 5 × 37 × 61 = 270,840
22 × 32 × 53 × 61 = 274,500
53 × 37 × 61 = 282,125
22 × 34 × 52 × 37 = 299,700
33 × 5 × 37 × 61 = 304,695
24 × 32 × 37 × 61 = 325,008
23 × 33 × 52 × 61 = 329,400
23 × 32 × 53 × 37 = 333,000
2 × 3 × 52 × 37 × 61 = 338,550
2 × 34 × 37 × 61 = 365,634
24 × 3 × 53 × 61 = 366,000
34 × 53 × 37 = 374,625
24 × 34 × 5 × 61 = 395,280
24 × 33 × 52 × 37 = 399,600
22 × 32 × 5 × 37 × 61 = 406,260
2 × 33 × 53 × 61 = 411,750
23 × 52 × 37 × 61 = 451,400
23 × 33 × 37 × 61 = 487,512
22 × 34 × 52 × 61 = 494,100
22 × 33 × 53 × 37 = 499,500
32 × 52 × 37 × 61 = 507,825
24 × 3 × 5 × 37 × 61 = 541,680
23 × 32 × 53 × 61 = 549,000
2 × 53 × 37 × 61 = 564,250
23 × 34 × 52 × 37 = 599,400
2 × 33 × 5 × 37 × 61 = 609,390
34 × 53 × 61 = 617,625
24 × 33 × 52 × 61 = 658,800
24 × 32 × 53 × 37 = 666,000
22 × 3 × 52 × 37 × 61 = 677,100
22 × 34 × 37 × 61 = 731,268
2 × 34 × 53 × 37 = 749,250
23 × 32 × 5 × 37 × 61 = 812,520
22 × 33 × 53 × 61 = 823,500
3 × 53 × 37 × 61 = 846,375
24 × 52 × 37 × 61 = 902,800
34 × 5 × 37 × 61 = 914,085
24 × 33 × 37 × 61 = 975,024
23 × 34 × 52 × 61 = 988,200
23 × 33 × 53 × 37 = 999,000
2 × 32 × 52 × 37 × 61 = 1,015,650
24 × 32 × 53 × 61 = 1,098,000
22 × 53 × 37 × 61 = 1,128,500
24 × 34 × 52 × 37 = 1,198,800
22 × 33 × 5 × 37 × 61 = 1,218,780
2 × 34 × 53 × 61 = 1,235,250
23 × 3 × 52 × 37 × 61 = 1,354,200
23 × 34 × 37 × 61 = 1,462,536
22 × 34 × 53 × 37 = 1,498,500
33 × 52 × 37 × 61 = 1,523,475
24 × 32 × 5 × 37 × 61 = 1,625,040
23 × 33 × 53 × 61 = 1,647,000
2 × 3 × 53 × 37 × 61 = 1,692,750
2 × 34 × 5 × 37 × 61 = 1,828,170
24 × 34 × 52 × 61 = 1,976,400
24 × 33 × 53 × 37 = 1,998,000
22 × 32 × 52 × 37 × 61 = 2,031,300
23 × 53 × 37 × 61 = 2,257,000
23 × 33 × 5 × 37 × 61 = 2,437,560
22 × 34 × 53 × 61 = 2,470,500
32 × 53 × 37 × 61 = 2,539,125
24 × 3 × 52 × 37 × 61 = 2,708,400
24 × 34 × 37 × 61 = 2,925,072
23 × 34 × 53 × 37 = 2,997,000
2 × 33 × 52 × 37 × 61 = 3,046,950
24 × 33 × 53 × 61 = 3,294,000
22 × 3 × 53 × 37 × 61 = 3,385,500
22 × 34 × 5 × 37 × 61 = 3,656,340
23 × 32 × 52 × 37 × 61 = 4,062,600
24 × 53 × 37 × 61 = 4,514,000
34 × 52 × 37 × 61 = 4,570,425
24 × 33 × 5 × 37 × 61 = 4,875,120
23 × 34 × 53 × 61 = 4,941,000
2 × 32 × 53 × 37 × 61 = 5,078,250
24 × 34 × 53 × 37 = 5,994,000
22 × 33 × 52 × 37 × 61 = 6,093,900
23 × 3 × 53 × 37 × 61 = 6,771,000
23 × 34 × 5 × 37 × 61 = 7,312,680
33 × 53 × 37 × 61 = 7,617,375
24 × 32 × 52 × 37 × 61 = 8,125,200
2 × 34 × 52 × 37 × 61 = 9,140,850
24 × 34 × 53 × 61 = 9,882,000
22 × 32 × 53 × 37 × 61 = 10,156,500
23 × 33 × 52 × 37 × 61 = 12,187,800
24 × 3 × 53 × 37 × 61 = 13,542,000
24 × 34 × 5 × 37 × 61 = 14,625,360
2 × 33 × 53 × 37 × 61 = 15,234,750
22 × 34 × 52 × 37 × 61 = 18,281,700
23 × 32 × 53 × 37 × 61 = 20,313,000
34 × 53 × 37 × 61 = 22,852,125
24 × 33 × 52 × 37 × 61 = 24,375,600
22 × 33 × 53 × 37 × 61 = 30,469,500
23 × 34 × 52 × 37 × 61 = 36,563,400
24 × 32 × 53 × 37 × 61 = 40,626,000
2 × 34 × 53 × 37 × 61 = 45,704,250
23 × 33 × 53 × 37 × 61 = 60,939,000
24 × 34 × 52 × 37 × 61 = 73,126,800
22 × 34 × 53 × 37 × 61 = 91,408,500
24 × 33 × 53 × 37 × 61 = 121,878,000
23 × 34 × 53 × 37 × 61 = 182,817,000
24 × 34 × 53 × 37 × 61 = 365,634,000

Final answer:

1,828,170,000 and 2,193,804,000 have 400 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 15; 16; 18; 20; 24; 25; 27; 30; 36; 37; 40; 45; 48; 50; 54; 60; 61; 72; 74; 75; 80; 81; 90; 100; 108; 111; 120; 122; 125; 135; 144; 148; 150; 162; 180; 183; 185; 200; 216; 222; 225; 240; 244; 250; 270; 296; 300; 305; 324; 333; 360; 366; 370; 375; 400; 405; 432; 444; 450; 488; 500; 540; 549; 555; 592; 600; 610; 648; 666; 675; 720; 732; 740; 750; 810; 888; 900; 915; 925; 976; 999; 1,000; 1,080; 1,098; 1,110; 1,125; 1,200; 1,220; 1,296; 1,332; 1,350; 1,464; 1,480; 1,500; 1,525; 1,620; 1,647; 1,665; 1,776; 1,800; 1,830; 1,850; 1,998; 2,000; 2,025; 2,160; 2,196; 2,220; 2,250; 2,257; 2,440; 2,664; 2,700; 2,745; 2,775; 2,928; 2,960; 2,997; 3,000; 3,050; 3,240; 3,294; 3,330; 3,375; 3,600; 3,660; 3,700; 3,996; 4,050; 4,392; 4,440; 4,500; 4,514; 4,575; 4,625; 4,880; 4,941; 4,995; 5,328; 5,400; 5,490; 5,550; 5,994; 6,000; 6,100; 6,480; 6,588; 6,660; 6,750; 6,771; 7,320; 7,400; 7,625; 7,992; 8,100; 8,235; 8,325; 8,784; 8,880; 9,000; 9,028; 9,150; 9,250; 9,882; 9,990; 10,125; 10,800; 10,980; 11,100; 11,285; 11,988; 12,200; 13,176; 13,320; 13,500; 13,542; 13,725; 13,875; 14,640; 14,800; 14,985; 15,250; 15,984; 16,200; 16,470; 16,650; 18,000; 18,056; 18,300; 18,500; 19,764; 19,980; 20,250; 20,313; 21,960; 22,200; 22,570; 22,875; 23,976; 24,400; 24,705; 24,975; 26,352; 26,640; 27,000; 27,084; 27,450; 27,750; 29,970; 30,500; 32,400; 32,940; 33,300; 33,855; 36,112; 36,600; 37,000; 39,528; 39,960; 40,500; 40,626; 41,175; 41,625; 43,920; 44,400; 45,140; 45,750; 47,952; 49,410; 49,950; 54,000; 54,168; 54,900; 55,500; 56,425; 59,940; 60,939; 61,000; 65,880; 66,600; 67,710; 68,625; 73,200; 74,000; 74,925; 79,056; 79,920; 81,000; 81,252; 82,350; 83,250; 90,280; 91,500; 98,820; 99,900; 101,565; 108,336; 109,800; 111,000; 112,850; 119,880; 121,878; 122,000; 123,525; 124,875; 131,760; 133,200; 135,420; 137,250; 149,850; 162,000; 162,504; 164,700; 166,500; 169,275; 180,560; 182,817; 183,000; 197,640; 199,800; 203,130; 205,875; 219,600; 222,000; 225,700; 239,760; 243,756; 247,050; 249,750; 270,840; 274,500; 282,125; 299,700; 304,695; 325,008; 329,400; 333,000; 338,550; 365,634; 366,000; 374,625; 395,280; 399,600; 406,260; 411,750; 451,400; 487,512; 494,100; 499,500; 507,825; 541,680; 549,000; 564,250; 599,400; 609,390; 617,625; 658,800; 666,000; 677,100; 731,268; 749,250; 812,520; 823,500; 846,375; 902,800; 914,085; 975,024; 988,200; 999,000; 1,015,650; 1,098,000; 1,128,500; 1,198,800; 1,218,780; 1,235,250; 1,354,200; 1,462,536; 1,498,500; 1,523,475; 1,625,040; 1,647,000; 1,692,750; 1,828,170; 1,976,400; 1,998,000; 2,031,300; 2,257,000; 2,437,560; 2,470,500; 2,539,125; 2,708,400; 2,925,072; 2,997,000; 3,046,950; 3,294,000; 3,385,500; 3,656,340; 4,062,600; 4,514,000; 4,570,425; 4,875,120; 4,941,000; 5,078,250; 5,994,000; 6,093,900; 6,771,000; 7,312,680; 7,617,375; 8,125,200; 9,140,850; 9,882,000; 10,156,500; 12,187,800; 13,542,000; 14,625,360; 15,234,750; 18,281,700; 20,313,000; 22,852,125; 24,375,600; 30,469,500; 36,563,400; 40,626,000; 45,704,250; 60,939,000; 73,126,800; 91,408,500; 121,878,000; 182,817,000 and 365,634,000
out of which 5 prime factors: 2; 3; 5; 37 and 61

The key to find the divisors of a number is to build its prime factorization.


Then determine all the different combinations (multiplications) of the prime factors, and their exponents, if any.



More operations of this kind:

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Tutoring: 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 "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

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 both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 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, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

  • 1,260 = 22 × 32;
  • 3,024 = 24 × 32 × 7;
  • 5,544 = 23 × 32 × 7 × 11;
  • Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;

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).

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".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples