What is the Greatest Common Factor of 31712 and 31722?

Greatest common factor (GCF) of 31712 and 31722 is 2.

GCF(31712,31722) = 2

We will now calculate the prime factors of 31712 and 31722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31712 and 31722.

How to find the GCF of 31712 and 31722?

We will first find the prime factorization of 31712 and 31722. After we will calculate the factors of 31712 and 31722 and find the biggest common factor number .

Step-1: Prime Factorization of 31712

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

31712 = 2⁵ × 991¹

Step-2: Prime Factorization of 31722

Prime factors of 31722 are 2, 3, 17, 311. Prime factorization of 31722 in exponential form is:

31722 = 2¹ × 3¹ × 17¹ × 311¹

Step-3: Factors of 31712

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

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

Step-4: Factors of 31722

List of positive integer factors of 31722 that divides 31712 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 311, 622, 933, 1866, 5287, 10574, 15861

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31712 and 31722. The biggest common factor number is the GCF number.
So the greatest common factor 31712 and 31722 is 2.

Also check out the Least Common Multiple of 31712 and 31722