What is the Greatest Common Factor of 38736 and 38752?

Greatest common factor (GCF) of 38736 and 38752 is 16.

GCF(38736,38752) = 16

We will now calculate the prime factors of 38736 and 38752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38736 and 38752.

How to find the GCF of 38736 and 38752?

We will first find the prime factorization of 38736 and 38752. After we will calculate the factors of 38736 and 38752 and find the biggest common factor number .

Step-1: Prime Factorization of 38736

Prime factors of 38736 are 2, 3, 269. Prime factorization of 38736 in exponential form is:

38736 = 2⁴ × 3² × 269¹

Step-2: Prime Factorization of 38752

Prime factors of 38752 are 2, 7, 173. Prime factorization of 38752 in exponential form is:

38752 = 2⁵ × 7¹ × 173¹

Step-3: Factors of 38736

List of positive integer factors of 38736 that divides 38736 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 269, 538, 807, 1076, 1614, 2152, 2421, 3228, 4304, 4842, 6456, 9684, 12912, 19368

Step-4: Factors of 38752

List of positive integer factors of 38752 that divides 38736 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 173, 224, 346, 692, 1211, 1384, 2422, 2768, 4844, 5536, 9688, 19376

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38736 and 38752. The biggest common factor number is the GCF number.
So the greatest common factor 38736 and 38752 is 16.

Also check out the Least Common Multiple of 38736 and 38752