What is the Greatest Common Factor of 31914 and 31928?

Greatest common factor (GCF) of 31914 and 31928 is 2.

GCF(31914,31928) = 2

We will now calculate the prime factors of 31914 and 31928, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31914 and 31928.

How to find the GCF of 31914 and 31928?

We will first find the prime factorization of 31914 and 31928. After we will calculate the factors of 31914 and 31928 and find the biggest common factor number .

Step-1: Prime Factorization of 31914

Prime factors of 31914 are 2, 3, 197. Prime factorization of 31914 in exponential form is:

31914 = 2¹ × 3⁴ × 197¹

Step-2: Prime Factorization of 31928

Prime factors of 31928 are 2, 13, 307. Prime factorization of 31928 in exponential form is:

31928 = 2³ × 13¹ × 307¹

Step-3: Factors of 31914

List of positive integer factors of 31914 that divides 31914 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 197, 394, 591, 1182, 1773, 3546, 5319, 10638, 15957

Step-4: Factors of 31928

List of positive integer factors of 31928 that divides 31914 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104, 307, 614, 1228, 2456, 3991, 7982, 15964

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31914 and 31928. The biggest common factor number is the GCF number.
So the greatest common factor 31914 and 31928 is 2.

Also check out the Least Common Multiple of 31914 and 31928