What is the Greatest Common Factor of 49674 and 49680?

Greatest common factor (GCF) of 49674 and 49680 is 6.

GCF(49674,49680) = 6

We will now calculate the prime factors of 49674 and 49680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49674 and 49680.

How to find the GCF of 49674 and 49680?

We will first find the prime factorization of 49674 and 49680. After we will calculate the factors of 49674 and 49680 and find the biggest common factor number .

Step-1: Prime Factorization of 49674

Prime factors of 49674 are 2, 3, 17, 487. Prime factorization of 49674 in exponential form is:

49674 = 2¹ × 3¹ × 17¹ × 487¹

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 49674

List of positive integer factors of 49674 that divides 49674 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 487, 974, 1461, 2922, 8279, 16558, 24837

Step-4: Factors of 49680

List of positive integer factors of 49680 that divides 49674 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 49674 and 49680. The biggest common factor number is the GCF number.
So the greatest common factor 49674 and 49680 is 6.

Also check out the Least Common Multiple of 49674 and 49680