What is the Greatest Common Factor of 57120 and 57135?

Greatest common factor (GCF) of 57120 and 57135 is 15.

GCF(57120,57135) = 15

We will now calculate the prime factors of 57120 and 57135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57120 and 57135.

How to find the GCF of 57120 and 57135?

We will first find the prime factorization of 57120 and 57135. After we will calculate the factors of 57120 and 57135 and find the biggest common factor number .

Step-1: Prime Factorization of 57120

Prime factors of 57120 are 2, 3, 5, 7, 17. Prime factorization of 57120 in exponential form is:

57120 = 2⁵ × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 57135

Prime factors of 57135 are 3, 5, 13, 293. Prime factorization of 57135 in exponential form is:

57135 = 3¹ × 5¹ × 13¹ × 293¹

Step-3: Factors of 57120

List of positive integer factors of 57120 that divides 57120 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 20, 21, 24, 28, 30, 32, 34, 35, 40, 42, 48, 51, 56, 60, 68, 70, 80, 84, 85, 96, 102, 105, 112, 119, 120, 136, 140, 160, 168, 170, 204, 210, 224, 238, 240, 255, 272, 280, 336, 340, 357, 408, 420, 476, 480, 510, 544, 560, 595, 672, 680, 714, 816, 840, 952, 1020, 1120, 1190, 1360, 1428, 1632, 1680, 1785, 1904, 2040, 2380, 2720, 2856, 3360, 3570, 3808, 4080, 4760, 5712, 7140, 8160, 9520, 11424, 14280, 19040, 28560

Step-4: Factors of 57135

List of positive integer factors of 57135 that divides 57120 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 293, 879, 1465, 3809, 4395, 11427, 19045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57120 and 57135. The biggest common factor number is the GCF number.
So the greatest common factor 57120 and 57135 is 15.

Also check out the Least Common Multiple of 57120 and 57135