What is the Greatest Common Factor of 51974 and 51984?

Greatest common factor (GCF) of 51974 and 51984 is 2.

GCF(51974,51984) = 2

We will now calculate the prime factors of 51974 and 51984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51974 and 51984.

How to find the GCF of 51974 and 51984?

We will first find the prime factorization of 51974 and 51984. After we will calculate the factors of 51974 and 51984 and find the biggest common factor number .

Step-1: Prime Factorization of 51974

Prime factors of 51974 are 2, 13, 1999. Prime factorization of 51974 in exponential form is:

51974 = 2¹ × 13¹ × 1999¹

Step-2: Prime Factorization of 51984

Prime factors of 51984 are 2, 3, 19. Prime factorization of 51984 in exponential form is:

51984 = 2⁴ × 3² × 19²

Step-3: Factors of 51974

List of positive integer factors of 51974 that divides 51974 without a remainder.

1, 2, 13, 26, 1999, 3998, 25987

Step-4: Factors of 51984

List of positive integer factors of 51984 that divides 51974 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 36, 38, 48, 57, 72, 76, 114, 144, 152, 171, 228, 304, 342, 361, 456, 684, 722, 912, 1083, 1368, 1444, 2166, 2736, 2888, 3249, 4332, 5776, 6498, 8664, 12996, 17328, 25992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51974 and 51984. The biggest common factor number is the GCF number.
So the greatest common factor 51974 and 51984 is 2.

Also check out the Least Common Multiple of 51974 and 51984