Greatest Common Factor of 314 and 321

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 314, 321 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 314 and 321 is 1.

GCF(314,321) = 1

GCF of 314 and 321

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

GCF of:
and

Greatest Common Factor of 314 and 321

GCF of 314 and 321 is 1

Prime Factorization of 314


2 314
157 157
1

Prime factors of 314 are 2,157. Prime factorization of 314 in exponential form is:

314 = 21×1571

Prime Factorization of 321


3 321
107 107
1

Prime factors of 321 are 3,107. Prime factorization of 321 in exponential form is:

321 = 31×1071

∴ So by taking common prime factors GCF of 314 and 321 is 1

Greatest Common Factor of 314 and 321 by matching factors method

Factors of 314

List of positive integer factors of 314 that divides 314 without a remainder.

1,2,157,314

Factors of 321

List of positive integer factors of 321 that divides 321 without a remainder.

1,3,107,321

Greatest Common Factor

We found the factors and prime factorization of 314 and 321. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 321 is 1.

Also check out the Least Common Multiple of 314 and 321

Properties of GCF 314 and 321

(i) The GCF of 314 and 321 is associative

GCF of 314 and 321 = GCF of 321 and 314

Related Greatest Common Factor of 314

Related Greatest Common Factor of 321

Frequently Asked Questions on GCF of 314 and 321

1. What is the GCF of 314 and 321?

Answer: GCF of 314 and 321 is 1.

2. What are the Factors of 314?

Answer: Factors of 314 are 1, 2, 157, 314. There are 4 integers that are factors of 314. The greatest factor of 314 is 314.

3. What are the Factors of 321?

Answer: Factors of 321 are 1, 3, 107, 321. There are 4 integers that are factors of 321. The greatest factor of 321 is 321.

4. How to Find the GCF of 314 and 321?

Answer:

Greatest Common Factor of 314 and 321 = 1

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 321

321 = 3 x 107

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 314 and 321 is 1