What is the Greatest Common Factor of 82972 and 82992?

Greatest common factor (GCF) of 82972 and 82992 is 4.

GCF(82972,82992) = 4

We will now calculate the prime factors of 82972 and 82992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82972 and 82992.

How to find the GCF of 82972 and 82992?

We will first find the prime factorization of 82972 and 82992. After we will calculate the factors of 82972 and 82992 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 82992

Prime factors of 82992 are 2, 3, 7, 13, 19. Prime factorization of 82992 in exponential form is:

82992 = 2⁴ × 3¹ × 7¹ × 13¹ × 19¹

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 82992

List of positive integer factors of 82992 that divides 82972 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 19, 21, 24, 26, 28, 38, 39, 42, 48, 52, 56, 57, 76, 78, 84, 91, 104, 112, 114, 133, 152, 156, 168, 182, 208, 228, 247, 266, 273, 304, 312, 336, 364, 399, 456, 494, 532, 546, 624, 728, 741, 798, 912, 988, 1064, 1092, 1456, 1482, 1596, 1729, 1976, 2128, 2184, 2964, 3192, 3458, 3952, 4368, 5187, 5928, 6384, 6916, 10374, 11856, 13832, 20748, 27664, 41496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82972 and 82992. The biggest common factor number is the GCF number.
So the greatest common factor 82972 and 82992 is 4.

Also check out the Least Common Multiple of 82972 and 82992