What is the Greatest Common Factor of 38112 and 38128?

Greatest common factor (GCF) of 38112 and 38128 is 16.

GCF(38112,38128) = 16

We will now calculate the prime factors of 38112 and 38128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38112 and 38128.

How to find the GCF of 38112 and 38128?

We will first find the prime factorization of 38112 and 38128. After we will calculate the factors of 38112 and 38128 and find the biggest common factor number .

Step-1: Prime Factorization of 38112

Prime factors of 38112 are 2, 3, 397. Prime factorization of 38112 in exponential form is:

38112 = 2⁵ × 3¹ × 397¹

Step-2: Prime Factorization of 38128

Prime factors of 38128 are 2, 2383. Prime factorization of 38128 in exponential form is:

38128 = 2⁴ × 2383¹

Step-3: Factors of 38112

List of positive integer factors of 38112 that divides 38112 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 397, 794, 1191, 1588, 2382, 3176, 4764, 6352, 9528, 12704, 19056

Step-4: Factors of 38128

List of positive integer factors of 38128 that divides 38112 without a remainder.

1, 2, 4, 8, 16, 2383, 4766, 9532, 19064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38112 and 38128. The biggest common factor number is the GCF number.
So the greatest common factor 38112 and 38128 is 16.

Also check out the Least Common Multiple of 38112 and 38128