What is the Greatest Common Factor of 49680 and 49700?

Greatest common factor (GCF) of 49680 and 49700 is 20.

GCF(49680,49700) = 20

We will now calculate the prime factors of 49680 and 49700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49680 and 49700.

How to find the GCF of 49680 and 49700?

We will first find the prime factorization of 49680 and 49700. After we will calculate the factors of 49680 and 49700 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 49700

Prime factors of 49700 are 2, 5, 7, 71. Prime factorization of 49700 in exponential form is:

49700 = 2² × 5² × 7¹ × 71¹

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 49700

List of positive integer factors of 49700 that divides 49680 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 71, 100, 140, 142, 175, 284, 350, 355, 497, 700, 710, 994, 1420, 1775, 1988, 2485, 3550, 4970, 7100, 9940, 12425, 24850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49680 and 49700. The biggest common factor number is the GCF number.
So the greatest common factor 49680 and 49700 is 20.

Also check out the Least Common Multiple of 49680 and 49700