What is the Greatest Common Factor of 57180 and 57200?

Greatest common factor (GCF) of 57180 and 57200 is 20.

GCF(57180,57200) = 20

We will now calculate the prime factors of 57180 and 57200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57180 and 57200.

How to find the GCF of 57180 and 57200?

We will first find the prime factorization of 57180 and 57200. After we will calculate the factors of 57180 and 57200 and find the biggest common factor number .

Step-1: Prime Factorization of 57180

Prime factors of 57180 are 2, 3, 5, 953. Prime factorization of 57180 in exponential form is:

57180 = 2² × 3¹ × 5¹ × 953¹

Step-2: Prime Factorization of 57200

Prime factors of 57200 are 2, 5, 11, 13. Prime factorization of 57200 in exponential form is:

57200 = 2⁴ × 5² × 11¹ × 13¹

Step-3: Factors of 57180

List of positive integer factors of 57180 that divides 57180 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 953, 1906, 2859, 3812, 4765, 5718, 9530, 11436, 14295, 19060, 28590

Step-4: Factors of 57200

List of positive integer factors of 57200 that divides 57180 without a remainder.

1, 2, 4, 5, 8, 10, 11, 13, 16, 20, 22, 25, 26, 40, 44, 50, 52, 55, 65, 80, 88, 100, 104, 110, 130, 143, 176, 200, 208, 220, 260, 275, 286, 325, 400, 440, 520, 550, 572, 650, 715, 880, 1040, 1100, 1144, 1300, 1430, 2200, 2288, 2600, 2860, 3575, 4400, 5200, 5720, 7150, 11440, 14300, 28600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57180 and 57200. The biggest common factor number is the GCF number.
So the greatest common factor 57180 and 57200 is 20.

Also check out the Least Common Multiple of 57180 and 57200