What is the Greatest Common Factor of 11970 and 11988?

Greatest common factor (GCF) of 11970 and 11988 is 18.

GCF(11970,11988) = 18

We will now calculate the prime factors of 11970 and 11988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11970 and 11988.

How to find the GCF of 11970 and 11988?

We will first find the prime factorization of 11970 and 11988. After we will calculate the factors of 11970 and 11988 and find the biggest common factor number .

Step-1: Prime Factorization of 11970

Prime factors of 11970 are 2, 3, 5, 7, 19. Prime factorization of 11970 in exponential form is:

11970 = 2¹ × 3² × 5¹ × 7¹ × 19¹

Step-2: Prime Factorization of 11988

Prime factors of 11988 are 2, 3, 37. Prime factorization of 11988 in exponential form is:

11988 = 2² × 3⁴ × 37¹

Step-3: Factors of 11970

List of positive integer factors of 11970 that divides 11970 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 19, 21, 30, 35, 38, 42, 45, 57, 63, 70, 90, 95, 105, 114, 126, 133, 171, 190, 210, 266, 285, 315, 342, 399, 570, 630, 665, 798, 855, 1197, 1330, 1710, 1995, 2394, 3990, 5985

Step-4: Factors of 11988

List of positive integer factors of 11988 that divides 11970 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 81, 108, 111, 148, 162, 222, 324, 333, 444, 666, 999, 1332, 1998, 2997, 3996, 5994

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11970 and 11988. The biggest common factor number is the GCF number.
So the greatest common factor 11970 and 11988 is 18.

Also check out the Least Common Multiple of 11970 and 11988