What is the Greatest Common Factor of 18960 and 18972?

Greatest common factor (GCF) of 18960 and 18972 is 12.

GCF(18960,18972) = 12

We will now calculate the prime factors of 18960 and 18972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18960 and 18972.

How to find the GCF of 18960 and 18972?

We will first find the prime factorization of 18960 and 18972. After we will calculate the factors of 18960 and 18972 and find the biggest common factor number .

Step-1: Prime Factorization of 18960

Prime factors of 18960 are 2, 3, 5, 79. Prime factorization of 18960 in exponential form is:

18960 = 2⁴ × 3¹ × 5¹ × 79¹

Step-2: Prime Factorization of 18972

Prime factors of 18972 are 2, 3, 17, 31. Prime factorization of 18972 in exponential form is:

18972 = 2² × 3² × 17¹ × 31¹

Step-3: Factors of 18960

List of positive integer factors of 18960 that divides 18960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 79, 80, 120, 158, 237, 240, 316, 395, 474, 632, 790, 948, 1185, 1264, 1580, 1896, 2370, 3160, 3792, 4740, 6320, 9480

Step-4: Factors of 18972

List of positive integer factors of 18972 that divides 18960 without a remainder.

1, 2, 3, 4, 6, 9, 12, 17, 18, 31, 34, 36, 51, 62, 68, 93, 102, 124, 153, 186, 204, 279, 306, 372, 527, 558, 612, 1054, 1116, 1581, 2108, 3162, 4743, 6324, 9486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18960 and 18972. The biggest common factor number is the GCF number.
So the greatest common factor 18960 and 18972 is 12.

Also check out the Least Common Multiple of 18960 and 18972