What is the Greatest Common Factor of 38688 and 38704?

Greatest common factor (GCF) of 38688 and 38704 is 16.

GCF(38688,38704) = 16

We will now calculate the prime factors of 38688 and 38704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38688 and 38704.

How to find the GCF of 38688 and 38704?

We will first find the prime factorization of 38688 and 38704. After we will calculate the factors of 38688 and 38704 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 38704

Prime factors of 38704 are 2, 41, 59. Prime factorization of 38704 in exponential form is:

38704 = 2⁴ × 41¹ × 59¹

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 38704

List of positive integer factors of 38704 that divides 38688 without a remainder.

1, 2, 4, 8, 16, 41, 59, 82, 118, 164, 236, 328, 472, 656, 944, 2419, 4838, 9676, 19352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38688 and 38704. The biggest common factor number is the GCF number.
So the greatest common factor 38688 and 38704 is 16.

Also check out the Least Common Multiple of 38688 and 38704