Greatest Common Factor of 314 and 322

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, 322 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 314 and 322 is 2.

GCF(314,322) = 2

GCF of 314 and 322

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

GCF of:
and

Greatest Common Factor of 314 and 322

GCF of 314 and 322 is 2

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 322


2 322
7 161
23 23
1

Prime factors of 322 are 2,7,23. Prime factorization of 322 in exponential form is:

322 = 21×71×231

∴ So by taking common prime factors GCF of 314 and 322 is 2

Greatest Common Factor of 314 and 322 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 322

List of positive integer factors of 322 that divides 322 without a remainder.

1,2,7,14,23,46,161,322

Greatest Common Factor

We found the factors and prime factorization of 314 and 322. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 322 is 2.

Also check out the Least Common Multiple of 314 and 322

Properties of GCF 314 and 322

(i) The GCF of 314 and 322 is associative

GCF of 314 and 322 = GCF of 322 and 314

Related Greatest Common Factor of 314

Related Greatest Common Factor of 322

Frequently Asked Questions on GCF of 314 and 322

1. What is the GCF of 314 and 322?

Answer: GCF of 314 and 322 is 2.

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 322?

Answer: Factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322. There are 8 integers that are factors of 322. The greatest factor of 322 is 322.

4. How to Find the GCF of 314 and 322?

Answer:

Greatest Common Factor of 314 and 322 = 2

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 322

322 = 2 x 7 x 23

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

GCF = 2

Step 4: Therefore, the greatest common factor of 314 and 322 is 2