What is the Greatest Common Factor of 31597 and 31616?

Greatest common factor (GCF) of 31597 and 31616 is 19.

GCF(31597,31616) = 19

We will now calculate the prime factors of 31597 and 31616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31597 and 31616.

How to find the GCF of 31597 and 31616?

We will first find the prime factorization of 31597 and 31616. After we will calculate the factors of 31597 and 31616 and find the biggest common factor number .

Step-1: Prime Factorization of 31597

Prime factors of 31597 are 19, 1663. Prime factorization of 31597 in exponential form is:

31597 = 19¹ × 1663¹

Step-2: 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-3: Factors of 31597

List of positive integer factors of 31597 that divides 31597 without a remainder.

1, 19, 1663

Step-4: Factors of 31616

List of positive integer factors of 31616 that divides 31597 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31597 and 31616. The biggest common factor number is the GCF number.
So the greatest common factor 31597 and 31616 is 19.

Also check out the Least Common Multiple of 31597 and 31616