What is the Greatest Common Factor of 57120 and 57140?

Greatest common factor (GCF) of 57120 and 57140 is 20.

GCF(57120,57140) = 20

We will now calculate the prime factors of 57120 and 57140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57120 and 57140.

How to find the GCF of 57120 and 57140?

We will first find the prime factorization of 57120 and 57140. After we will calculate the factors of 57120 and 57140 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 57140

Prime factors of 57140 are 2, 5, 2857. Prime factorization of 57140 in exponential form is:

57140 = 2² × 5¹ × 2857¹

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 57140

List of positive integer factors of 57140 that divides 57120 without a remainder.

1, 2, 4, 5, 10, 20, 2857, 5714, 11428, 14285, 28570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57120 and 57140. The biggest common factor number is the GCF number.
So the greatest common factor 57120 and 57140 is 20.

Also check out the Least Common Multiple of 57120 and 57140