What is the Greatest Common Factor of 49974 and 49980?

Greatest common factor (GCF) of 49974 and 49980 is 6.

GCF(49974,49980) = 6

We will now calculate the prime factors of 49974 and 49980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49974 and 49980.

How to find the GCF of 49974 and 49980?

We will first find the prime factorization of 49974 and 49980. After we will calculate the factors of 49974 and 49980 and find the biggest common factor number .

Step-1: Prime Factorization of 49974

Prime factors of 49974 are 2, 3, 8329. Prime factorization of 49974 in exponential form is:

49974 = 2¹ × 3¹ × 8329¹

Step-2: Prime Factorization of 49980

Prime factors of 49980 are 2, 3, 5, 7, 17. Prime factorization of 49980 in exponential form is:

49980 = 2² × 3¹ × 5¹ × 7² × 17¹

Step-3: Factors of 49974

List of positive integer factors of 49974 that divides 49974 without a remainder.

1, 2, 3, 6, 8329, 16658, 24987

Step-4: Factors of 49980

List of positive integer factors of 49980 that divides 49974 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 49, 51, 60, 68, 70, 84, 85, 98, 102, 105, 119, 140, 147, 170, 196, 204, 210, 238, 245, 255, 294, 340, 357, 420, 476, 490, 510, 588, 595, 714, 735, 833, 980, 1020, 1190, 1428, 1470, 1666, 1785, 2380, 2499, 2940, 3332, 3570, 4165, 4998, 7140, 8330, 9996, 12495, 16660, 24990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49974 and 49980. The biggest common factor number is the GCF number.
So the greatest common factor 49974 and 49980 is 6.

Also check out the Least Common Multiple of 49974 and 49980