What is the Greatest Common Factor of 27131 and 27144?

Greatest common factor (GCF) of 27131 and 27144 is 13.

GCF(27131,27144) = 13

We will now calculate the prime factors of 27131 and 27144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27131 and 27144.

How to find the GCF of 27131 and 27144?

We will first find the prime factorization of 27131 and 27144. After we will calculate the factors of 27131 and 27144 and find the biggest common factor number .

Step-1: Prime Factorization of 27131

Prime factors of 27131 are 13, 2087. Prime factorization of 27131 in exponential form is:

27131 = 13¹ × 2087¹

Step-2: Prime Factorization of 27144

Prime factors of 27144 are 2, 3, 13, 29. Prime factorization of 27144 in exponential form is:

27144 = 2³ × 3² × 13¹ × 29¹

Step-3: Factors of 27131

List of positive integer factors of 27131 that divides 27131 without a remainder.

1, 13, 2087

Step-4: Factors of 27144

List of positive integer factors of 27144 that divides 27131 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 29, 36, 39, 52, 58, 72, 78, 87, 104, 116, 117, 156, 174, 232, 234, 261, 312, 348, 377, 468, 522, 696, 754, 936, 1044, 1131, 1508, 2088, 2262, 3016, 3393, 4524, 6786, 9048, 13572

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27131 and 27144. The biggest common factor number is the GCF number.
So the greatest common factor 27131 and 27144 is 13.

Also check out the Least Common Multiple of 27131 and 27144