What is the Greatest Common Factor of 71964 and 71982?

Greatest common factor (GCF) of 71964 and 71982 is 18.

GCF(71964,71982) = 18

We will now calculate the prime factors of 71964 and 71982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71964 and 71982.

How to find the GCF of 71964 and 71982?

We will first find the prime factorization of 71964 and 71982. After we will calculate the factors of 71964 and 71982 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 71982

Prime factors of 71982 are 2, 3, 31, 43. Prime factorization of 71982 in exponential form is:

71982 = 2¹ × 3³ × 31¹ × 43¹

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 71982

List of positive integer factors of 71982 that divides 71964 without a remainder.

1, 2, 3, 6, 9, 18, 27, 31, 43, 54, 62, 86, 93, 129, 186, 258, 279, 387, 558, 774, 837, 1161, 1333, 1674, 2322, 2666, 3999, 7998, 11997, 23994, 35991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71964 and 71982. The biggest common factor number is the GCF number.
So the greatest common factor 71964 and 71982 is 18.

Also check out the Least Common Multiple of 71964 and 71982