What is the Greatest Common Factor of 14972 and 14980?

Greatest common factor (GCF) of 14972 and 14980 is 4.

GCF(14972,14980) = 4

We will now calculate the prime factors of 14972 and 14980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14972 and 14980.

How to find the GCF of 14972 and 14980?

We will first find the prime factorization of 14972 and 14980. After we will calculate the factors of 14972 and 14980 and find the biggest common factor number .

Step-1: Prime Factorization of 14972

Prime factors of 14972 are 2, 19, 197. Prime factorization of 14972 in exponential form is:

14972 = 2² × 19¹ × 197¹

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 14972

List of positive integer factors of 14972 that divides 14972 without a remainder.

1, 2, 4, 19, 38, 76, 197, 394, 788, 3743, 7486

Step-4: Factors of 14980

List of positive integer factors of 14980 that divides 14972 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 14972 and 14980. The biggest common factor number is the GCF number.
So the greatest common factor 14972 and 14980 is 4.

Also check out the Least Common Multiple of 14972 and 14980