What is the Greatest Common Factor of 82972 and 82984?

Greatest common factor (GCF) of 82972 and 82984 is 4.

GCF(82972,82984) = 4

We will now calculate the prime factors of 82972 and 82984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82972 and 82984.

How to find the GCF of 82972 and 82984?

We will first find the prime factorization of 82972 and 82984. After we will calculate the factors of 82972 and 82984 and find the biggest common factor number .

Step-1: Prime Factorization of 82972

Prime factors of 82972 are 2, 20743. Prime factorization of 82972 in exponential form is:

82972 = 2² × 20743¹

Step-2: Prime Factorization of 82984

Prime factors of 82984 are 2, 11, 23, 41. Prime factorization of 82984 in exponential form is:

82984 = 2³ × 11¹ × 23¹ × 41¹

Step-3: Factors of 82972

List of positive integer factors of 82972 that divides 82972 without a remainder.

1, 2, 4, 20743, 41486

Step-4: Factors of 82984

List of positive integer factors of 82984 that divides 82972 without a remainder.

1, 2, 4, 8, 11, 22, 23, 41, 44, 46, 82, 88, 92, 164, 184, 253, 328, 451, 506, 902, 943, 1012, 1804, 1886, 2024, 3608, 3772, 7544, 10373, 20746, 41492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82972 and 82984. The biggest common factor number is the GCF number.
So the greatest common factor 82972 and 82984 is 4.

Also check out the Least Common Multiple of 82972 and 82984