What is the Greatest Common Factor of 14972 and 14991?

Greatest common factor (GCF) of 14972 and 14991 is 19.

GCF(14972,14991) = 19

We will now calculate the prime factors of 14972 and 14991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14972 and 14991.

How to find the GCF of 14972 and 14991?

We will first find the prime factorization of 14972 and 14991. After we will calculate the factors of 14972 and 14991 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 14991

Prime factors of 14991 are 3, 19, 263. Prime factorization of 14991 in exponential form is:

14991 = 3¹ × 19¹ × 263¹

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 14991

List of positive integer factors of 14991 that divides 14972 without a remainder.

1, 3, 19, 57, 263, 789, 4997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14972 and 14991. The biggest common factor number is the GCF number.
So the greatest common factor 14972 and 14991 is 19.

Also check out the Least Common Multiple of 14972 and 14991