What is the Greatest Common Factor of 11760 and 11772?

Greatest common factor (GCF) of 11760 and 11772 is 12.

GCF(11760,11772) = 12

We will now calculate the prime factors of 11760 and 11772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11760 and 11772.

How to find the GCF of 11760 and 11772?

We will first find the prime factorization of 11760 and 11772. After we will calculate the factors of 11760 and 11772 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 11772

Prime factors of 11772 are 2, 3, 109. Prime factorization of 11772 in exponential form is:

11772 = 2² × 3³ × 109¹

Step-3: Factors of 11760

List of positive integer factors of 11760 that divides 11760 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

Step-4: Factors of 11772

List of positive integer factors of 11772 that divides 11760 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 109, 218, 327, 436, 654, 981, 1308, 1962, 2943, 3924, 5886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11760 and 11772. The biggest common factor number is the GCF number.
So the greatest common factor 11760 and 11772 is 12.

Also check out the Least Common Multiple of 11760 and 11772