What is the Greatest Common Factor of 27954 and 27972?

Greatest common factor (GCF) of 27954 and 27972 is 18.

GCF(27954,27972) = 18

We will now calculate the prime factors of 27954 and 27972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27954 and 27972.

How to find the GCF of 27954 and 27972?

We will first find the prime factorization of 27954 and 27972. After we will calculate the factors of 27954 and 27972 and find the biggest common factor number .

Step-1: Prime Factorization of 27954

Prime factors of 27954 are 2, 3, 1553. Prime factorization of 27954 in exponential form is:

27954 = 2¹ × 3² × 1553¹

Step-2: 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-3: Factors of 27954

List of positive integer factors of 27954 that divides 27954 without a remainder.

1, 2, 3, 6, 9, 18, 1553, 3106, 4659, 9318, 13977

Step-4: Factors of 27972

List of positive integer factors of 27972 that divides 27954 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27954 and 27972. The biggest common factor number is the GCF number.
So the greatest common factor 27954 and 27972 is 18.

Also check out the Least Common Multiple of 27954 and 27972