What is the Greatest Common Factor of 38800 and 38816?

Greatest common factor (GCF) of 38800 and 38816 is 16.

GCF(38800,38816) = 16

We will now calculate the prime factors of 38800 and 38816, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38800 and 38816.

How to find the GCF of 38800 and 38816?

We will first find the prime factorization of 38800 and 38816. After we will calculate the factors of 38800 and 38816 and find the biggest common factor number .

Step-1: Prime Factorization of 38800

Prime factors of 38800 are 2, 5, 97. Prime factorization of 38800 in exponential form is:

38800 = 2⁴ × 5² × 97¹

Step-2: Prime Factorization of 38816

Prime factors of 38816 are 2, 1213. Prime factorization of 38816 in exponential form is:

38816 = 2⁵ × 1213¹

Step-3: Factors of 38800

List of positive integer factors of 38800 that divides 38800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 97, 100, 194, 200, 388, 400, 485, 776, 970, 1552, 1940, 2425, 3880, 4850, 7760, 9700, 19400

Step-4: Factors of 38816

List of positive integer factors of 38816 that divides 38800 without a remainder.

1, 2, 4, 8, 16, 32, 1213, 2426, 4852, 9704, 19408

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38800 and 38816. The biggest common factor number is the GCF number.
So the greatest common factor 38800 and 38816 is 16.

Also check out the Least Common Multiple of 38800 and 38816