What is the Greatest Common Factor of 14736 and 14754?

Greatest common factor (GCF) of 14736 and 14754 is 6.

GCF(14736,14754) = 6

We will now calculate the prime factors of 14736 and 14754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14736 and 14754.

How to find the GCF of 14736 and 14754?

We will first find the prime factorization of 14736 and 14754. After we will calculate the factors of 14736 and 14754 and find the biggest common factor number .

Step-1: Prime Factorization of 14736

Prime factors of 14736 are 2, 3, 307. Prime factorization of 14736 in exponential form is:

14736 = 2⁴ × 3¹ × 307¹

Step-2: Prime Factorization of 14754

Prime factors of 14754 are 2, 3, 2459. Prime factorization of 14754 in exponential form is:

14754 = 2¹ × 3¹ × 2459¹

Step-3: Factors of 14736

List of positive integer factors of 14736 that divides 14736 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 307, 614, 921, 1228, 1842, 2456, 3684, 4912, 7368

Step-4: Factors of 14754

List of positive integer factors of 14754 that divides 14736 without a remainder.

1, 2, 3, 6, 2459, 4918, 7377

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14736 and 14754. The biggest common factor number is the GCF number.
So the greatest common factor 14736 and 14754 is 6.

Also check out the Least Common Multiple of 14736 and 14754