What is the Greatest Common Factor of 38675 and 38688?

Greatest common factor (GCF) of 38675 and 38688 is 13.

GCF(38675,38688) = 13

We will now calculate the prime factors of 38675 and 38688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38675 and 38688.

How to find the GCF of 38675 and 38688?

We will first find the prime factorization of 38675 and 38688. After we will calculate the factors of 38675 and 38688 and find the biggest common factor number .

Step-1: Prime Factorization of 38675

Prime factors of 38675 are 5, 7, 13, 17. Prime factorization of 38675 in exponential form is:

38675 = 5² × 7¹ × 13¹ × 17¹

Step-2: 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-3: Factors of 38675

List of positive integer factors of 38675 that divides 38675 without a remainder.

1, 5, 7, 13, 17, 25, 35, 65, 85, 91, 119, 175, 221, 325, 425, 455, 595, 1105, 1547, 2275, 2975, 5525, 7735

Step-4: Factors of 38688

List of positive integer factors of 38688 that divides 38675 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38675 and 38688. The biggest common factor number is the GCF number.
So the greatest common factor 38675 and 38688 is 13.

Also check out the Least Common Multiple of 38675 and 38688