What is the Greatest Common Factor of 57189 and 57200?

Greatest common factor (GCF) of 57189 and 57200 is 11.

GCF(57189,57200) = 11

We will now calculate the prime factors of 57189 and 57200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57189 and 57200.

How to find the GCF of 57189 and 57200?

We will first find the prime factorization of 57189 and 57200. After we will calculate the factors of 57189 and 57200 and find the biggest common factor number .

Step-1: Prime Factorization of 57189

Prime factors of 57189 are 3, 11, 1733. Prime factorization of 57189 in exponential form is:

57189 = 3¹ × 11¹ × 1733¹

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 57189

List of positive integer factors of 57189 that divides 57189 without a remainder.

1, 3, 11, 33, 1733, 5199, 19063

Step-4: Factors of 57200

List of positive integer factors of 57200 that divides 57189 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 57189 and 57200. The biggest common factor number is the GCF number.
So the greatest common factor 57189 and 57200 is 11.

Also check out the Least Common Multiple of 57189 and 57200