What is the Greatest Common Factor of 14974 and 14980?

Greatest common factor (GCF) of 14974 and 14980 is 2.

GCF(14974,14980) = 2

We will now calculate the prime factors of 14974 and 14980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14974 and 14980.

How to find the GCF of 14974 and 14980?

We will first find the prime factorization of 14974 and 14980. After we will calculate the factors of 14974 and 14980 and find the biggest common factor number .

Step-1: Prime Factorization of 14974

Prime factors of 14974 are 2, 7487. Prime factorization of 14974 in exponential form is:

14974 = 2¹ × 7487¹

Step-2: Prime Factorization of 14980

Prime factors of 14980 are 2, 5, 7, 107. Prime factorization of 14980 in exponential form is:

14980 = 2² × 5¹ × 7¹ × 107¹

Step-3: Factors of 14974

List of positive integer factors of 14974 that divides 14974 without a remainder.

1, 2, 7487

Step-4: Factors of 14980

List of positive integer factors of 14980 that divides 14974 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 107, 140, 214, 428, 535, 749, 1070, 1498, 2140, 2996, 3745, 7490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14974 and 14980. The biggest common factor number is the GCF number.
So the greatest common factor 14974 and 14980 is 2.

Also check out the Least Common Multiple of 14974 and 14980