What is the Greatest Common Factor of 38670 and 38688?

Greatest common factor (GCF) of 38670 and 38688 is 6.

GCF(38670,38688) = 6

We will now calculate the prime factors of 38670 and 38688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38670 and 38688.

How to find the GCF of 38670 and 38688?

We will first find the prime factorization of 38670 and 38688. After we will calculate the factors of 38670 and 38688 and find the biggest common factor number .

Step-1: Prime Factorization of 38670

Prime factors of 38670 are 2, 3, 5, 1289. Prime factorization of 38670 in exponential form is:

38670 = 2¹ × 3¹ × 5¹ × 1289¹

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 38670

List of positive integer factors of 38670 that divides 38670 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1289, 2578, 3867, 6445, 7734, 12890, 19335

Step-4: Factors of 38688

List of positive integer factors of 38688 that divides 38670 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 38670 and 38688. The biggest common factor number is the GCF number.
So the greatest common factor 38670 and 38688 is 6.

Also check out the Least Common Multiple of 38670 and 38688