What is the Greatest Common Factor of 14970 and 14976?

Greatest common factor (GCF) of 14970 and 14976 is 6.

GCF(14970,14976) = 6

We will now calculate the prime factors of 14970 and 14976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14970 and 14976.

How to find the GCF of 14970 and 14976?

We will first find the prime factorization of 14970 and 14976. After we will calculate the factors of 14970 and 14976 and find the biggest common factor number .

Step-1: Prime Factorization of 14970

Prime factors of 14970 are 2, 3, 5, 499. Prime factorization of 14970 in exponential form is:

14970 = 2¹ × 3¹ × 5¹ × 499¹

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 14970

List of positive integer factors of 14970 that divides 14970 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 499, 998, 1497, 2495, 2994, 4990, 7485

Step-4: Factors of 14976

List of positive integer factors of 14976 that divides 14970 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 14970 and 14976. The biggest common factor number is the GCF number.
So the greatest common factor 14970 and 14976 is 6.

Also check out the Least Common Multiple of 14970 and 14976