What is the Greatest Common Factor of 31624 and 31642?

Greatest common factor (GCF) of 31624 and 31642 is 2.

GCF(31624,31642) = 2

We will now calculate the prime factors of 31624 and 31642, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31624 and 31642.

How to find the GCF of 31624 and 31642?

We will first find the prime factorization of 31624 and 31642. After we will calculate the factors of 31624 and 31642 and find the biggest common factor number .

Step-1: Prime Factorization of 31624

Prime factors of 31624 are 2, 59, 67. Prime factorization of 31624 in exponential form is:

31624 = 2³ × 59¹ × 67¹

Step-2: Prime Factorization of 31642

Prime factors of 31642 are 2, 13, 1217. Prime factorization of 31642 in exponential form is:

31642 = 2¹ × 13¹ × 1217¹

Step-3: Factors of 31624

List of positive integer factors of 31624 that divides 31624 without a remainder.

1, 2, 4, 8, 59, 67, 118, 134, 236, 268, 472, 536, 3953, 7906, 15812

Step-4: Factors of 31642

List of positive integer factors of 31642 that divides 31624 without a remainder.

1, 2, 13, 26, 1217, 2434, 15821

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31624 and 31642. The biggest common factor number is the GCF number.
So the greatest common factor 31624 and 31642 is 2.

Also check out the Least Common Multiple of 31624 and 31642