What is the Greatest Common Factor of 38688 and 38701?

Greatest common factor (GCF) of 38688 and 38701 is 13.

GCF(38688,38701) = 13

We will now calculate the prime factors of 38688 and 38701, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38688 and 38701.

How to find the GCF of 38688 and 38701?

We will first find the prime factorization of 38688 and 38701. After we will calculate the factors of 38688 and 38701 and find the biggest common factor number .

Step-1: Prime Factorization of 38688

Prime factors of 38688 are 2, 3, 13, 31. Prime factorization of 38688 in exponential form is:

38688 = 2⁵ × 3¹ × 13¹ × 31¹

Step-2: Prime Factorization of 38701

Prime factors of 38701 are 13, 229. Prime factorization of 38701 in exponential form is:

38701 = 13² × 229¹

Step-3: Factors of 38688

List of positive integer factors of 38688 that divides 38688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52, 62, 78, 93, 96, 104, 124, 156, 186, 208, 248, 312, 372, 403, 416, 496, 624, 744, 806, 992, 1209, 1248, 1488, 1612, 2418, 2976, 3224, 4836, 6448, 9672, 12896, 19344

Step-4: Factors of 38701

List of positive integer factors of 38701 that divides 38688 without a remainder.

1, 13, 169, 229, 2977

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38688 and 38701. The biggest common factor number is the GCF number.
So the greatest common factor 38688 and 38701 is 13.

Also check out the Least Common Multiple of 38688 and 38701