What is the Greatest Common Factor of 51968 and 51984?

Greatest common factor (GCF) of 51968 and 51984 is 16.

GCF(51968,51984) = 16

We will now calculate the prime factors of 51968 and 51984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51968 and 51984.

How to find the GCF of 51968 and 51984?

We will first find the prime factorization of 51968 and 51984. After we will calculate the factors of 51968 and 51984 and find the biggest common factor number .

Step-1: Prime Factorization of 51968

Prime factors of 51968 are 2, 7, 29. Prime factorization of 51968 in exponential form is:

51968 = 2⁸ × 7¹ × 29¹

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 51968

List of positive integer factors of 51968 that divides 51968 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 29, 32, 56, 58, 64, 112, 116, 128, 203, 224, 232, 256, 406, 448, 464, 812, 896, 928, 1624, 1792, 1856, 3248, 3712, 6496, 7424, 12992, 25984

Step-4: Factors of 51984

List of positive integer factors of 51984 that divides 51968 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 51968 and 51984. The biggest common factor number is the GCF number.
So the greatest common factor 51968 and 51984 is 16.

Also check out the Least Common Multiple of 51968 and 51984