Greatest Common Factor of 357 and 364

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 357, 364 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 357 and 364 is 7.

GCF(357,364) = 7

GCF of 357 and 364

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

GCF of:
and

Greatest Common Factor of 357 and 364

GCF of 357 and 364 is 7

Prime Factorization of 357


3 357
7 119
17 17
1

Prime factors of 357 are 3,7,17. Prime factorization of 357 in exponential form is:

357 = 31×71×171

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

∴ So by taking common prime factors GCF of 357 and 364 is 7

Greatest Common Factor of 357 and 364 by matching factors method

Factors of 357

List of positive integer factors of 357 that divides 357 without a remainder.

1,3,7,17,21,51,119,357

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

Greatest Common Factor

We found the factors and prime factorization of 357 and 364. The biggest common factor number is the GCF number.
So the greatest common factor 357 and 364 is 7.

Also check out the Least Common Multiple of 357 and 364

Properties of GCF 357 and 364

(i) The GCF of 357 and 364 is associative

GCF of 357 and 364 = GCF of 364 and 357

Related Greatest Common Factor of 357

Related Greatest Common Factor of 364

Frequently Asked Questions on GCF of 357 and 364

1. What is the GCF of 357 and 364?

Answer: GCF of 357 and 364 is 7.

2. What are the Factors of 357?

Answer: Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357. There are 8 integers that are factors of 357. The greatest factor of 357 is 357.

3. 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.

4. How to Find the GCF of 357 and 364?

Answer:

Greatest Common Factor of 357 and 364 = 7

Step 1: Find the prime factorization of 357

357 = 3 x 7 x 17

Step 2: Find the prime factorization of 364

364 = 2 x 2 x 7 x 13

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 357 and 364 is 7