What is the Greatest Common Factor of 38640 and 38656?

Greatest common factor (GCF) of 38640 and 38656 is 16.

GCF(38640,38656) = 16

We will now calculate the prime factors of 38640 and 38656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38640 and 38656.

How to find the GCF of 38640 and 38656?

We will first find the prime factorization of 38640 and 38656. After we will calculate the factors of 38640 and 38656 and find the biggest common factor number .

Step-1: Prime Factorization of 38640

Prime factors of 38640 are 2, 3, 5, 7, 23. Prime factorization of 38640 in exponential form is:

38640 = 2⁴ × 3¹ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 38656

Prime factors of 38656 are 2, 151. Prime factorization of 38656 in exponential form is:

38656 = 2⁸ × 151¹

Step-3: Factors of 38640

List of positive integer factors of 38640 that divides 38640 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 105, 112, 115, 120, 138, 140, 161, 168, 184, 210, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 483, 552, 560, 644, 690, 805, 840, 920, 966, 1104, 1288, 1380, 1610, 1680, 1840, 1932, 2415, 2576, 2760, 3220, 3864, 4830, 5520, 6440, 7728, 9660, 12880, 19320

Step-4: Factors of 38656

List of positive integer factors of 38656 that divides 38640 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 151, 256, 302, 604, 1208, 2416, 4832, 9664, 19328

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38640 and 38656. The biggest common factor number is the GCF number.
So the greatest common factor 38640 and 38656 is 16.

Also check out the Least Common Multiple of 38640 and 38656