What is the Greatest Common Factor of 27984 and 27996?

Greatest common factor (GCF) of 27984 and 27996 is 12.

GCF(27984,27996) = 12

We will now calculate the prime factors of 27984 and 27996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27984 and 27996.

How to find the GCF of 27984 and 27996?

We will first find the prime factorization of 27984 and 27996. After we will calculate the factors of 27984 and 27996 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27996

Prime factors of 27996 are 2, 3, 2333. Prime factorization of 27996 in exponential form is:

27996 = 2² × 3¹ × 2333¹

Step-3: Factors of 27984

List of positive integer factors of 27984 that divides 27984 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

Step-4: Factors of 27996

List of positive integer factors of 27996 that divides 27984 without a remainder.

1, 2, 3, 4, 6, 12, 2333, 4666, 6999, 9332, 13998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27984 and 27996. The biggest common factor number is the GCF number.
So the greatest common factor 27984 and 27996 is 12.

Also check out the Least Common Multiple of 27984 and 27996