What is the Greatest Common Factor of 31600 and 31616?

Greatest common factor (GCF) of 31600 and 31616 is 16.

GCF(31600,31616) = 16

We will now calculate the prime factors of 31600 and 31616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31600 and 31616.

How to find the GCF of 31600 and 31616?

We will first find the prime factorization of 31600 and 31616. After we will calculate the factors of 31600 and 31616 and find the biggest common factor number .

Step-1: Prime Factorization of 31600

Prime factors of 31600 are 2, 5, 79. Prime factorization of 31600 in exponential form is:

31600 = 2⁴ × 5² × 79¹

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 31600

List of positive integer factors of 31600 that divides 31600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 79, 80, 100, 158, 200, 316, 395, 400, 632, 790, 1264, 1580, 1975, 3160, 3950, 6320, 7900, 15800

Step-4: Factors of 31616

List of positive integer factors of 31616 that divides 31600 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 31600 and 31616. The biggest common factor number is the GCF number.
So the greatest common factor 31600 and 31616 is 16.

Also check out the Least Common Multiple of 31600 and 31616