What is the Greatest Common Factor of 7974 and 7980?

Greatest common factor (GCF) of 7974 and 7980 is 6.

GCF(7974,7980) = 6

We will now calculate the prime factors of 7974 and 7980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7974 and 7980.

How to find the GCF of 7974 and 7980?

We will first find the prime factorization of 7974 and 7980. After we will calculate the factors of 7974 and 7980 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7980

Prime factors of 7980 are 2, 3, 5, 7, 19. Prime factorization of 7980 in exponential form is:

7980 = 2² × 3¹ × 5¹ × 7¹ × 19¹

Step-3: Factors of 7974

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

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

Step-4: Factors of 7980

List of positive integer factors of 7980 that divides 7974 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 28, 30, 35, 38, 42, 57, 60, 70, 76, 84, 95, 105, 114, 133, 140, 190, 210, 228, 266, 285, 380, 399, 420, 532, 570, 665, 798, 1140, 1330, 1596, 1995, 2660, 3990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7974 and 7980. The biggest common factor number is the GCF number.
So the greatest common factor 7974 and 7980 is 6.

Also check out the Least Common Multiple of 7974 and 7980