What is the Greatest Common Factor of 14748 and 14760?

Greatest common factor (GCF) of 14748 and 14760 is 12.

GCF(14748,14760) = 12

We will now calculate the prime factors of 14748 and 14760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14748 and 14760.

How to find the GCF of 14748 and 14760?

We will first find the prime factorization of 14748 and 14760. After we will calculate the factors of 14748 and 14760 and find the biggest common factor number .

Step-1: Prime Factorization of 14748

Prime factors of 14748 are 2, 3, 1229. Prime factorization of 14748 in exponential form is:

14748 = 2² × 3¹ × 1229¹

Step-2: Prime Factorization of 14760

Prime factors of 14760 are 2, 3, 5, 41. Prime factorization of 14760 in exponential form is:

14760 = 2³ × 3² × 5¹ × 41¹

Step-3: Factors of 14748

List of positive integer factors of 14748 that divides 14748 without a remainder.

1, 2, 3, 4, 6, 12, 1229, 2458, 3687, 4916, 7374

Step-4: Factors of 14760

List of positive integer factors of 14760 that divides 14748 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 41, 45, 60, 72, 82, 90, 120, 123, 164, 180, 205, 246, 328, 360, 369, 410, 492, 615, 738, 820, 984, 1230, 1476, 1640, 1845, 2460, 2952, 3690, 4920, 7380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14748 and 14760. The biggest common factor number is the GCF number.
So the greatest common factor 14748 and 14760 is 12.

Also check out the Least Common Multiple of 14748 and 14760