What is the Greatest Common Factor of 49680 and 49696?

Greatest common factor (GCF) of 49680 and 49696 is 16.

GCF(49680,49696) = 16

We will now calculate the prime factors of 49680 and 49696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49680 and 49696.

How to find the GCF of 49680 and 49696?

We will first find the prime factorization of 49680 and 49696. After we will calculate the factors of 49680 and 49696 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49696

Prime factors of 49696 are 2, 1553. Prime factorization of 49696 in exponential form is:

49696 = 2⁵ × 1553¹

Step-3: Factors of 49680

List of positive integer factors of 49680 that divides 49680 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

Step-4: Factors of 49696

List of positive integer factors of 49696 that divides 49680 without a remainder.

1, 2, 4, 8, 16, 32, 1553, 3106, 6212, 12424, 24848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49680 and 49696. The biggest common factor number is the GCF number.
So the greatest common factor 49680 and 49696 is 16.

Also check out the Least Common Multiple of 49680 and 49696