What is the Greatest Common Factor of 71964 and 71980?

Greatest common factor (GCF) of 71964 and 71980 is 4.

GCF(71964,71980) = 4

We will now calculate the prime factors of 71964 and 71980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71964 and 71980.

How to find the GCF of 71964 and 71980?

We will first find the prime factorization of 71964 and 71980. After we will calculate the factors of 71964 and 71980 and find the biggest common factor number .

Step-1: Prime Factorization of 71964

Prime factors of 71964 are 2, 3, 1999. Prime factorization of 71964 in exponential form is:

71964 = 2² × 3² × 1999¹

Step-2: Prime Factorization of 71980

Prime factors of 71980 are 2, 5, 59, 61. Prime factorization of 71980 in exponential form is:

71980 = 2² × 5¹ × 59¹ × 61¹

Step-3: Factors of 71964

List of positive integer factors of 71964 that divides 71964 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1999, 3998, 5997, 7996, 11994, 17991, 23988, 35982

Step-4: Factors of 71980

List of positive integer factors of 71980 that divides 71964 without a remainder.

1, 2, 4, 5, 10, 20, 59, 61, 118, 122, 236, 244, 295, 305, 590, 610, 1180, 1220, 3599, 7198, 14396, 17995, 35990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71964 and 71980. The biggest common factor number is the GCF number.
So the greatest common factor 71964 and 71980 is 4.

Also check out the Least Common Multiple of 71964 and 71980