What is the Greatest Common Factor of 18972 and 18984?

Greatest common factor (GCF) of 18972 and 18984 is 12.

GCF(18972,18984) = 12

We will now calculate the prime factors of 18972 and 18984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18972 and 18984.

How to find the GCF of 18972 and 18984?

We will first find the prime factorization of 18972 and 18984. After we will calculate the factors of 18972 and 18984 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 18984

Prime factors of 18984 are 2, 3, 7, 113. Prime factorization of 18984 in exponential form is:

18984 = 2³ × 3¹ × 7¹ × 113¹

Step-3: Factors of 18972

List of positive integer factors of 18972 that divides 18972 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

Step-4: Factors of 18984

List of positive integer factors of 18984 that divides 18972 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 113, 168, 226, 339, 452, 678, 791, 904, 1356, 1582, 2373, 2712, 3164, 4746, 6328, 9492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18972 and 18984. The biggest common factor number is the GCF number.
So the greatest common factor 18972 and 18984 is 12.

Also check out the Least Common Multiple of 18972 and 18984