What is the Greatest Common Factor of 14976 and 14989?

Greatest common factor (GCF) of 14976 and 14989 is 13.

GCF(14976,14989) = 13

We will now calculate the prime factors of 14976 and 14989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14976 and 14989.

How to find the GCF of 14976 and 14989?

We will first find the prime factorization of 14976 and 14989. After we will calculate the factors of 14976 and 14989 and find the biggest common factor number .

Step-1: Prime Factorization of 14976

Prime factors of 14976 are 2, 3, 13. Prime factorization of 14976 in exponential form is:

14976 = 2⁷ × 3² × 13¹

Step-2: Prime Factorization of 14989

Prime factors of 14989 are 13, 1153. Prime factorization of 14989 in exponential form is:

14989 = 13¹ × 1153¹

Step-3: Factors of 14976

List of positive integer factors of 14976 that divides 14976 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 128, 144, 156, 192, 208, 234, 288, 312, 384, 416, 468, 576, 624, 832, 936, 1152, 1248, 1664, 1872, 2496, 3744, 4992, 7488

Step-4: Factors of 14989

List of positive integer factors of 14989 that divides 14976 without a remainder.

1, 13, 1153

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14976 and 14989. The biggest common factor number is the GCF number.
So the greatest common factor 14976 and 14989 is 13.

Also check out the Least Common Multiple of 14976 and 14989