What is the Greatest Common Factor of 14972 and 14976?

Greatest common factor (GCF) of 14972 and 14976 is 4.

GCF(14972,14976) = 4

We will now calculate the prime factors of 14972 and 14976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14972 and 14976.

How to find the GCF of 14972 and 14976?

We will first find the prime factorization of 14972 and 14976. After we will calculate the factors of 14972 and 14976 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 14976

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

14976 = 2⁷ × 3² × 13¹

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 14976

List of positive integer factors of 14976 that divides 14972 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14972 and 14976. The biggest common factor number is the GCF number.
So the greatest common factor 14972 and 14976 is 4.

Also check out the Least Common Multiple of 14972 and 14976