What is the Greatest Common Factor of 27999 and 28014?

Greatest common factor (GCF) of 27999 and 28014 is 3.

GCF(27999,28014) = 3

We will now calculate the prime factors of 27999 and 28014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27999 and 28014.

How to find the GCF of 27999 and 28014?

We will first find the prime factorization of 27999 and 28014. After we will calculate the factors of 27999 and 28014 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 28014

Prime factors of 28014 are 2, 3, 7, 23, 29. Prime factorization of 28014 in exponential form is:

28014 = 2¹ × 3¹ × 7¹ × 23¹ × 29¹

Step-3: Factors of 27999

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

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

Step-4: Factors of 28014

List of positive integer factors of 28014 that divides 27999 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 29, 42, 46, 58, 69, 87, 138, 161, 174, 203, 322, 406, 483, 609, 667, 966, 1218, 1334, 2001, 4002, 4669, 9338, 14007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27999 and 28014. The biggest common factor number is the GCF number.
So the greatest common factor 27999 and 28014 is 3.

Also check out the Least Common Multiple of 27999 and 28014