What is the Greatest Common Factor of 57200 and 57214?

Greatest common factor (GCF) of 57200 and 57214 is 2.

GCF(57200,57214) = 2

We will now calculate the prime factors of 57200 and 57214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57200 and 57214.

How to find the GCF of 57200 and 57214?

We will first find the prime factorization of 57200 and 57214. After we will calculate the factors of 57200 and 57214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 57214

Prime factors of 57214 are 2, 28607. Prime factorization of 57214 in exponential form is:

57214 = 2¹ × 28607¹

Step-3: Factors of 57200

List of positive integer factors of 57200 that divides 57200 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

Step-4: Factors of 57214

List of positive integer factors of 57214 that divides 57200 without a remainder.

1, 2, 28607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57200 and 57214. The biggest common factor number is the GCF number.
So the greatest common factor 57200 and 57214 is 2.

Also check out the Least Common Multiple of 57200 and 57214