What is the Greatest Common Factor of 82971 and 82980?

Greatest common factor (GCF) of 82971 and 82980 is 9.

GCF(82971,82980) = 9

We will now calculate the prime factors of 82971 and 82980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82971 and 82980.

How to find the GCF of 82971 and 82980?

We will first find the prime factorization of 82971 and 82980. After we will calculate the factors of 82971 and 82980 and find the biggest common factor number .

Step-1: Prime Factorization of 82971

Prime factors of 82971 are 3, 7, 439. Prime factorization of 82971 in exponential form is:

82971 = 3³ × 7¹ × 439¹

Step-2: Prime Factorization of 82980

Prime factors of 82980 are 2, 3, 5, 461. Prime factorization of 82980 in exponential form is:

82980 = 2² × 3² × 5¹ × 461¹

Step-3: Factors of 82971

List of positive integer factors of 82971 that divides 82971 without a remainder.

1, 3, 7, 9, 21, 27, 63, 189, 439, 1317, 3073, 3951, 9219, 11853, 27657

Step-4: Factors of 82980

List of positive integer factors of 82980 that divides 82971 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 461, 922, 1383, 1844, 2305, 2766, 4149, 4610, 5532, 6915, 8298, 9220, 13830, 16596, 20745, 27660, 41490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82971 and 82980. The biggest common factor number is the GCF number.
So the greatest common factor 82971 and 82980 is 9.

Also check out the Least Common Multiple of 82971 and 82980