What is the Greatest Common Factor of 38744 and 38752?

Greatest common factor (GCF) of 38744 and 38752 is 8.

GCF(38744,38752) = 8

We will now calculate the prime factors of 38744 and 38752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38744 and 38752.

How to find the GCF of 38744 and 38752?

We will first find the prime factorization of 38744 and 38752. After we will calculate the factors of 38744 and 38752 and find the biggest common factor number .

Step-1: Prime Factorization of 38744

Prime factors of 38744 are 2, 29, 167. Prime factorization of 38744 in exponential form is:

38744 = 2³ × 29¹ × 167¹

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 38744

List of positive integer factors of 38744 that divides 38744 without a remainder.

1, 2, 4, 8, 29, 58, 116, 167, 232, 334, 668, 1336, 4843, 9686, 19372

Step-4: Factors of 38752

List of positive integer factors of 38752 that divides 38744 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 38744 and 38752. The biggest common factor number is the GCF number.
So the greatest common factor 38744 and 38752 is 8.

Also check out the Least Common Multiple of 38744 and 38752