What is the Greatest Common Factor of 27984 and 27999?

Greatest common factor (GCF) of 27984 and 27999 is 3.

GCF(27984,27999) = 3

We will now calculate the prime factors of 27984 and 27999, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27984 and 27999.

How to find the GCF of 27984 and 27999?

We will first find the prime factorization of 27984 and 27999. After we will calculate the factors of 27984 and 27999 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 27999

Prime factors of 27999 are 3, 17, 61. Prime factorization of 27999 in exponential form is:

27999 = 3³ × 17¹ × 61¹

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 27999

List of positive integer factors of 27999 that divides 27984 without a remainder.

1, 3, 9, 17, 27, 51, 61, 153, 183, 459, 549, 1037, 1647, 3111, 9333

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27984 and 27999. The biggest common factor number is the GCF number.
So the greatest common factor 27984 and 27999 is 3.

Also check out the Least Common Multiple of 27984 and 27999