What is the Greatest Common Factor of 11970 and 11984?

Greatest common factor (GCF) of 11970 and 11984 is 14.

GCF(11970,11984) = 14

We will now calculate the prime factors of 11970 and 11984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11970 and 11984.

How to find the GCF of 11970 and 11984?

We will first find the prime factorization of 11970 and 11984. After we will calculate the factors of 11970 and 11984 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 11984

Prime factors of 11984 are 2, 7, 107. Prime factorization of 11984 in exponential form is:

11984 = 2⁴ × 7¹ × 107¹

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 11984

List of positive integer factors of 11984 that divides 11970 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 107, 112, 214, 428, 749, 856, 1498, 1712, 2996, 5992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11970 and 11984. The biggest common factor number is the GCF number.
So the greatest common factor 11970 and 11984 is 14.

Also check out the Least Common Multiple of 11970 and 11984