What is the Greatest Common Factor of 25700 and 25710?

Greatest common factor (GCF) of 25700 and 25710 is 10.

GCF(25700,25710) = 10

We will now calculate the prime factors of 25700 and 25710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25700 and 25710.

How to find the GCF of 25700 and 25710?

We will first find the prime factorization of 25700 and 25710. After we will calculate the factors of 25700 and 25710 and find the biggest common factor number .

Step-1: Prime Factorization of 25700

Prime factors of 25700 are 2, 5, 257. Prime factorization of 25700 in exponential form is:

25700 = 2² × 5² × 257¹

Step-2: Prime Factorization of 25710

Prime factors of 25710 are 2, 3, 5, 857. Prime factorization of 25710 in exponential form is:

25710 = 2¹ × 3¹ × 5¹ × 857¹

Step-3: Factors of 25700

List of positive integer factors of 25700 that divides 25700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 257, 514, 1028, 1285, 2570, 5140, 6425, 12850

Step-4: Factors of 25710

List of positive integer factors of 25710 that divides 25700 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 857, 1714, 2571, 4285, 5142, 8570, 12855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25700 and 25710. The biggest common factor number is the GCF number.
So the greatest common factor 25700 and 25710 is 10.

Also check out the Least Common Multiple of 25700 and 25710