What is the Greatest Common Factor of 7968 and 7974?

Greatest common factor (GCF) of 7968 and 7974 is 6.

GCF(7968,7974) = 6

We will now calculate the prime factors of 7968 and 7974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7968 and 7974.

How to find the GCF of 7968 and 7974?

We will first find the prime factorization of 7968 and 7974. After we will calculate the factors of 7968 and 7974 and find the biggest common factor number .

Step-1: Prime Factorization of 7968

Prime factors of 7968 are 2, 3, 83. Prime factorization of 7968 in exponential form is:

7968 = 2⁵ × 3¹ × 83¹

Step-2: Prime Factorization of 7974

Prime factors of 7974 are 2, 3, 443. Prime factorization of 7974 in exponential form is:

7974 = 2¹ × 3² × 443¹

Step-3: Factors of 7968

List of positive integer factors of 7968 that divides 7968 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 83, 96, 166, 249, 332, 498, 664, 996, 1328, 1992, 2656, 3984

Step-4: Factors of 7974

List of positive integer factors of 7974 that divides 7968 without a remainder.

1, 2, 3, 6, 9, 18, 443, 886, 1329, 2658, 3987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7968 and 7974. The biggest common factor number is the GCF number.
So the greatest common factor 7968 and 7974 is 6.

Also check out the Least Common Multiple of 7968 and 7974