What is the Greatest Common Factor of 11745 and 11760?

Greatest common factor (GCF) of 11745 and 11760 is 15.

GCF(11745,11760) = 15

We will now calculate the prime factors of 11745 and 11760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11745 and 11760.

How to find the GCF of 11745 and 11760?

We will first find the prime factorization of 11745 and 11760. After we will calculate the factors of 11745 and 11760 and find the biggest common factor number .

Step-1: Prime Factorization of 11745

Prime factors of 11745 are 3, 5, 29. Prime factorization of 11745 in exponential form is:

11745 = 3⁴ × 5¹ × 29¹

Step-2: Prime Factorization of 11760

Prime factors of 11760 are 2, 3, 5, 7. Prime factorization of 11760 in exponential form is:

11760 = 2⁴ × 3¹ × 5¹ × 7²

Step-3: Factors of 11745

List of positive integer factors of 11745 that divides 11745 without a remainder.

1, 3, 5, 9, 15, 27, 29, 45, 81, 87, 135, 145, 261, 405, 435, 783, 1305, 2349, 3915

Step-4: Factors of 11760

List of positive integer factors of 11760 that divides 11745 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 98, 105, 112, 120, 140, 147, 168, 196, 210, 240, 245, 280, 294, 336, 392, 420, 490, 560, 588, 735, 784, 840, 980, 1176, 1470, 1680, 1960, 2352, 2940, 3920, 5880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11745 and 11760. The biggest common factor number is the GCF number.
So the greatest common factor 11745 and 11760 is 15.

Also check out the Least Common Multiple of 11745 and 11760