What is the Greatest Common Factor of 31564 and 31582?

Greatest common factor (GCF) of 31564 and 31582 is 2.

GCF(31564,31582) = 2

We will now calculate the prime factors of 31564 and 31582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31564 and 31582.

How to find the GCF of 31564 and 31582?

We will first find the prime factorization of 31564 and 31582. After we will calculate the factors of 31564 and 31582 and find the biggest common factor number .

Step-1: Prime Factorization of 31564

Prime factors of 31564 are 2, 13, 607. Prime factorization of 31564 in exponential form is:

31564 = 2² × 13¹ × 607¹

Step-2: Prime Factorization of 31582

Prime factors of 31582 are 2, 15791. Prime factorization of 31582 in exponential form is:

31582 = 2¹ × 15791¹

Step-3: Factors of 31564

List of positive integer factors of 31564 that divides 31564 without a remainder.

1, 2, 4, 13, 26, 52, 607, 1214, 2428, 7891, 15782

Step-4: Factors of 31582

List of positive integer factors of 31582 that divides 31564 without a remainder.

1, 2, 15791

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31564 and 31582. The biggest common factor number is the GCF number.
So the greatest common factor 31564 and 31582 is 2.

Also check out the Least Common Multiple of 31564 and 31582