Greatest Common Factor of 364 and 371

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 364, 371 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 364 and 371 is 7.

GCF(364,371) = 7

GCF of 364 and 371

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 364 and 371

GCF of 364 and 371 is 7

Prime Factorization of 364


2 364
2 182
7 91
13 13
1

Prime factors of 364 are 2,7,13. Prime factorization of 364 in exponential form is:

364 = 22×71×131

Prime Factorization of 371


7 371
53 53
1

Prime factors of 371 are 7,53. Prime factorization of 371 in exponential form is:

371 = 71×531

∴ So by taking common prime factors GCF of 364 and 371 is 7

Greatest Common Factor of 364 and 371 by matching factors method

Factors of 364

List of positive integer factors of 364 that divides 364 without a remainder.

1,2,4,7,13,14,26,28,52,91,182,364

Factors of 371

List of positive integer factors of 371 that divides 371 without a remainder.

1,7,53,371

Greatest Common Factor

We found the factors and prime factorization of 364 and 371. The biggest common factor number is the GCF number.
So the greatest common factor 364 and 371 is 7.

Also check out the Least Common Multiple of 364 and 371

Properties of GCF 364 and 371

(i) The GCF of 364 and 371 is associative

GCF of 364 and 371 = GCF of 371 and 364

Related Greatest Common Factor of 364

Related Greatest Common Factor of 371

Frequently Asked Questions on GCF of 364 and 371

1. What is the GCF of 364 and 371?

Answer: GCF of 364 and 371 is 7.

2. What are the Factors of 364?

Answer: Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. There are 12 integers that are factors of 364. The greatest factor of 364 is 364.

3. What are the Factors of 371?

Answer: Factors of 371 are 1, 7, 53, 371. There are 4 integers that are factors of 371. The greatest factor of 371 is 371.

4. How to Find the GCF of 364 and 371?

Answer:

Greatest Common Factor of 364 and 371 = 7

Step 1: Find the prime factorization of 364

364 = 2 x 2 x 7 x 13

Step 2: Find the prime factorization of 371

371 = 7 x 53

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 7

Step 4: Therefore, the greatest common factor of 364 and 371 is 7