What is the Greatest Common Factor of 27314 and 27321?

Greatest common factor (GCF) of 27314 and 27321 is 7.

GCF(27314,27321) = 7

We will now calculate the prime factors of 27314 and 27321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27314 and 27321.

How to find the GCF of 27314 and 27321?

We will first find the prime factorization of 27314 and 27321. After we will calculate the factors of 27314 and 27321 and find the biggest common factor number .

Step-1: Prime Factorization of 27314

Prime factors of 27314 are 2, 7, 1951. Prime factorization of 27314 in exponential form is:

27314 = 2¹ × 7¹ × 1951¹

Step-2: Prime Factorization of 27321

Prime factors of 27321 are 3, 7, 1301. Prime factorization of 27321 in exponential form is:

27321 = 3¹ × 7¹ × 1301¹

Step-3: Factors of 27314

List of positive integer factors of 27314 that divides 27314 without a remainder.

1, 2, 7, 14, 1951, 3902, 13657

Step-4: Factors of 27321

List of positive integer factors of 27321 that divides 27314 without a remainder.

1, 3, 7, 21, 1301, 3903, 9107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27314 and 27321. The biggest common factor number is the GCF number.
So the greatest common factor 27314 and 27321 is 7.

Also check out the Least Common Multiple of 27314 and 27321