What is the Greatest Common Factor of 49680 and 49685?

Greatest common factor (GCF) of 49680 and 49685 is 5.

GCF(49680,49685) = 5

We will now calculate the prime factors of 49680 and 49685, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49680 and 49685.

How to find the GCF of 49680 and 49685?

We will first find the prime factorization of 49680 and 49685. After we will calculate the factors of 49680 and 49685 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 49685

Prime factors of 49685 are 5, 19, 523. Prime factorization of 49685 in exponential form is:

49685 = 5¹ × 19¹ × 523¹

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 49685

List of positive integer factors of 49685 that divides 49680 without a remainder.

1, 5, 19, 95, 523, 2615, 9937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49680 and 49685. The biggest common factor number is the GCF number.
So the greatest common factor 49680 and 49685 is 5.

Also check out the Least Common Multiple of 49680 and 49685