What is the Greatest Common Factor of 27972 and 27984?

Greatest common factor (GCF) of 27972 and 27984 is 12.

GCF(27972,27984) = 12

We will now calculate the prime factors of 27972 and 27984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27972 and 27984.

How to find the GCF of 27972 and 27984?

We will first find the prime factorization of 27972 and 27984. After we will calculate the factors of 27972 and 27984 and find the biggest common factor number .

Step-1: Prime Factorization of 27972

Prime factors of 27972 are 2, 3, 7, 37. Prime factorization of 27972 in exponential form is:

27972 = 2² × 3³ × 7¹ × 37¹

Step-2: Prime Factorization of 27984

Prime factors of 27984 are 2, 3, 11, 53. Prime factorization of 27984 in exponential form is:

27984 = 2⁴ × 3¹ × 11¹ × 53¹

Step-3: Factors of 27972

List of positive integer factors of 27972 that divides 27972 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 37, 42, 54, 63, 74, 84, 108, 111, 126, 148, 189, 222, 252, 259, 333, 378, 444, 518, 666, 756, 777, 999, 1036, 1332, 1554, 1998, 2331, 3108, 3996, 4662, 6993, 9324, 13986

Step-4: Factors of 27984

List of positive integer factors of 27984 that divides 27972 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 53, 66, 88, 106, 132, 159, 176, 212, 264, 318, 424, 528, 583, 636, 848, 1166, 1272, 1749, 2332, 2544, 3498, 4664, 6996, 9328, 13992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27972 and 27984. The biggest common factor number is the GCF number.
So the greatest common factor 27972 and 27984 is 12.

Also check out the Least Common Multiple of 27972 and 27984