What is the Greatest Common Factor of 31525 and 31538?

Greatest common factor (GCF) of 31525 and 31538 is 13.

GCF(31525,31538) = 13

We will now calculate the prime factors of 31525 and 31538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31525 and 31538.

How to find the GCF of 31525 and 31538?

We will first find the prime factorization of 31525 and 31538. After we will calculate the factors of 31525 and 31538 and find the biggest common factor number .

Step-1: Prime Factorization of 31525

Prime factors of 31525 are 5, 13, 97. Prime factorization of 31525 in exponential form is:

31525 = 5² × 13¹ × 97¹

Step-2: Prime Factorization of 31538

Prime factors of 31538 are 2, 13, 1213. Prime factorization of 31538 in exponential form is:

31538 = 2¹ × 13¹ × 1213¹

Step-3: Factors of 31525

List of positive integer factors of 31525 that divides 31525 without a remainder.

1, 5, 13, 25, 65, 97, 325, 485, 1261, 2425, 6305

Step-4: Factors of 31538

List of positive integer factors of 31538 that divides 31525 without a remainder.

1, 2, 13, 26, 1213, 2426, 15769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31525 and 31538. The biggest common factor number is the GCF number.
So the greatest common factor 31525 and 31538 is 13.

Also check out the Least Common Multiple of 31525 and 31538