What is the Greatest Common Factor of 49664 and 49680?

Greatest common factor (GCF) of 49664 and 49680 is 16.

GCF(49664,49680) = 16

We will now calculate the prime factors of 49664 and 49680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49664 and 49680.

How to find the GCF of 49664 and 49680?

We will first find the prime factorization of 49664 and 49680. After we will calculate the factors of 49664 and 49680 and find the biggest common factor number .

Step-1: Prime Factorization of 49664

Prime factors of 49664 are 2, 97. Prime factorization of 49664 in exponential form is:

49664 = 2⁹ × 97¹

Step-2: Prime Factorization of 49680

Prime factors of 49680 are 2, 3, 5, 23. Prime factorization of 49680 in exponential form is:

49680 = 2⁴ × 3³ × 5¹ × 23¹

Step-3: Factors of 49664

List of positive integer factors of 49664 that divides 49664 without a remainder.

1, 2, 4, 8, 16, 32, 64, 97, 128, 194, 256, 388, 512, 776, 1552, 3104, 6208, 12416, 24832

Step-4: Factors of 49680

List of positive integer factors of 49680 that divides 49664 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 27, 30, 36, 40, 45, 46, 48, 54, 60, 69, 72, 80, 90, 92, 108, 115, 120, 135, 138, 144, 180, 184, 207, 216, 230, 240, 270, 276, 345, 360, 368, 414, 432, 460, 540, 552, 621, 690, 720, 828, 920, 1035, 1080, 1104, 1242, 1380, 1656, 1840, 2070, 2160, 2484, 2760, 3105, 3312, 4140, 4968, 5520, 6210, 8280, 9936, 12420, 16560, 24840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49664 and 49680. The biggest common factor number is the GCF number.
So the greatest common factor 49664 and 49680 is 16.

Also check out the Least Common Multiple of 49664 and 49680