What is the Greatest Common Factor of 38738 and 38752?

Greatest common factor (GCF) of 38738 and 38752 is 14.

GCF(38738,38752) = 14

We will now calculate the prime factors of 38738 and 38752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38738 and 38752.

How to find the GCF of 38738 and 38752?

We will first find the prime factorization of 38738 and 38752. After we will calculate the factors of 38738 and 38752 and find the biggest common factor number .

Step-1: Prime Factorization of 38738

Prime factors of 38738 are 2, 7, 2767. Prime factorization of 38738 in exponential form is:

38738 = 2¹ × 7¹ × 2767¹

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 38738

List of positive integer factors of 38738 that divides 38738 without a remainder.

1, 2, 7, 14, 2767, 5534, 19369

Step-4: Factors of 38752

List of positive integer factors of 38752 that divides 38738 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 38738 and 38752. The biggest common factor number is the GCF number.
So the greatest common factor 38738 and 38752 is 14.

Also check out the Least Common Multiple of 38738 and 38752