What is the Greatest Common Factor of 38096 and 38112?

Greatest common factor (GCF) of 38096 and 38112 is 16.

GCF(38096,38112) = 16

We will now calculate the prime factors of 38096 and 38112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38096 and 38112.

How to find the GCF of 38096 and 38112?

We will first find the prime factorization of 38096 and 38112. After we will calculate the factors of 38096 and 38112 and find the biggest common factor number .

Step-1: Prime Factorization of 38096

Prime factors of 38096 are 2, 2381. Prime factorization of 38096 in exponential form is:

38096 = 2⁴ × 2381¹

Step-2: 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-3: Factors of 38096

List of positive integer factors of 38096 that divides 38096 without a remainder.

1, 2, 4, 8, 16, 2381, 4762, 9524, 19048

Step-4: Factors of 38112

List of positive integer factors of 38112 that divides 38096 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38096 and 38112. The biggest common factor number is the GCF number.
So the greatest common factor 38096 and 38112 is 16.

Also check out the Least Common Multiple of 38096 and 38112