What is the Greatest Common Factor of 38992 and 39008?

Greatest common factor (GCF) of 38992 and 39008 is 16.

GCF(38992,39008) = 16

We will now calculate the prime factors of 38992 and 39008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38992 and 39008.

How to find the GCF of 38992 and 39008?

We will first find the prime factorization of 38992 and 39008. After we will calculate the factors of 38992 and 39008 and find the biggest common factor number .

Step-1: Prime Factorization of 38992

Prime factors of 38992 are 2, 2437. Prime factorization of 38992 in exponential form is:

38992 = 2⁴ × 2437¹

Step-2: Prime Factorization of 39008

Prime factors of 39008 are 2, 23, 53. Prime factorization of 39008 in exponential form is:

39008 = 2⁵ × 23¹ × 53¹

Step-3: Factors of 38992

List of positive integer factors of 38992 that divides 38992 without a remainder.

1, 2, 4, 8, 16, 2437, 4874, 9748, 19496

Step-4: Factors of 39008

List of positive integer factors of 39008 that divides 38992 without a remainder.

1, 2, 4, 8, 16, 23, 32, 46, 53, 92, 106, 184, 212, 368, 424, 736, 848, 1219, 1696, 2438, 4876, 9752, 19504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38992 and 39008. The biggest common factor number is the GCF number.
So the greatest common factor 38992 and 39008 is 16.

Also check out the Least Common Multiple of 38992 and 39008