What is the Greatest Common Factor of 31616 and 31629?

Greatest common factor (GCF) of 31616 and 31629 is 13.

GCF(31616,31629) = 13

We will now calculate the prime factors of 31616 and 31629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31616 and 31629.

How to find the GCF of 31616 and 31629?

We will first find the prime factorization of 31616 and 31629. After we will calculate the factors of 31616 and 31629 and find the biggest common factor number .

Step-1: Prime Factorization of 31616

Prime factors of 31616 are 2, 13, 19. Prime factorization of 31616 in exponential form is:

31616 = 2⁷ × 13¹ × 19¹

Step-2: Prime Factorization of 31629

Prime factors of 31629 are 3, 13, 811. Prime factorization of 31629 in exponential form is:

31629 = 3¹ × 13¹ × 811¹

Step-3: Factors of 31616

List of positive integer factors of 31616 that divides 31616 without a remainder.

1, 2, 4, 8, 13, 16, 19, 26, 32, 38, 52, 64, 76, 104, 128, 152, 208, 247, 304, 416, 494, 608, 832, 988, 1216, 1664, 1976, 2432, 3952, 7904, 15808

Step-4: Factors of 31629

List of positive integer factors of 31629 that divides 31616 without a remainder.

1, 3, 13, 39, 811, 2433, 10543

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31616 and 31629. The biggest common factor number is the GCF number.
So the greatest common factor 31616 and 31629 is 13.

Also check out the Least Common Multiple of 31616 and 31629