What is the Greatest Common Factor of 82978 and 82992?

Greatest common factor (GCF) of 82978 and 82992 is 14.

GCF(82978,82992) = 14

We will now calculate the prime factors of 82978 and 82992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82978 and 82992.

How to find the GCF of 82978 and 82992?

We will first find the prime factorization of 82978 and 82992. After we will calculate the factors of 82978 and 82992 and find the biggest common factor number .

Step-1: Prime Factorization of 82978

Prime factors of 82978 are 2, 7, 5927. Prime factorization of 82978 in exponential form is:

82978 = 2¹ × 7¹ × 5927¹

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 82978

List of positive integer factors of 82978 that divides 82978 without a remainder.

1, 2, 7, 14, 5927, 11854, 41489

Step-4: Factors of 82992

List of positive integer factors of 82992 that divides 82978 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 82978 and 82992. The biggest common factor number is the GCF number.
So the greatest common factor 82978 and 82992 is 14.

Also check out the Least Common Multiple of 82978 and 82992