What is the Greatest Common Factor of 31696 and 31712?

Greatest common factor (GCF) of 31696 and 31712 is 16.

GCF(31696,31712) = 16

We will now calculate the prime factors of 31696 and 31712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31696 and 31712.

How to find the GCF of 31696 and 31712?

We will first find the prime factorization of 31696 and 31712. After we will calculate the factors of 31696 and 31712 and find the biggest common factor number .

Step-1: Prime Factorization of 31696

Prime factors of 31696 are 2, 7, 283. Prime factorization of 31696 in exponential form is:

31696 = 2⁴ × 7¹ × 283¹

Step-2: Prime Factorization of 31712

Prime factors of 31712 are 2, 991. Prime factorization of 31712 in exponential form is:

31712 = 2⁵ × 991¹

Step-3: Factors of 31696

List of positive integer factors of 31696 that divides 31696 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 283, 566, 1132, 1981, 2264, 3962, 4528, 7924, 15848

Step-4: Factors of 31712

List of positive integer factors of 31712 that divides 31696 without a remainder.

1, 2, 4, 8, 16, 32, 991, 1982, 3964, 7928, 15856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31696 and 31712. The biggest common factor number is the GCF number.
So the greatest common factor 31696 and 31712 is 16.

Also check out the Least Common Multiple of 31696 and 31712