Greatest Common Factor of 714 and 722

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 714, 722 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 714 and 722 is 2.

GCF(714,722) = 2

GCF of 714 and 722

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

GCF of:
and

Greatest Common Factor of 714 and 722

GCF of 714 and 722 is 2

Prime Factorization of 714


2 714
3 357
7 119
17 17
1

Prime factors of 714 are 2,3,7,17. Prime factorization of 714 in exponential form is:

714 = 21×31×71×171

Prime Factorization of 722


2 722
19 361
19 19
1

Prime factors of 722 are 2,19. Prime factorization of 722 in exponential form is:

722 = 21×192

∴ So by taking common prime factors GCF of 714 and 722 is 2

Greatest Common Factor of 714 and 722 by matching factors method

Factors of 714

List of positive integer factors of 714 that divides 714 without a remainder.

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Factors of 722

List of positive integer factors of 722 that divides 722 without a remainder.

1,2,19,38,361,722

Greatest Common Factor

We found the factors and prime factorization of 714 and 722. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 722 is 2.

Also check out the Least Common Multiple of 714 and 722

Properties of GCF 714 and 722

(i) The GCF of 714 and 722 is associative

GCF of 714 and 722 = GCF of 722 and 714

Related Greatest Common Factor of 714

Related Greatest Common Factor of 722

Frequently Asked Questions on GCF of 714 and 722

1. What is the GCF of 714 and 722?

Answer: GCF of 714 and 722 is 2.

2. What are the Factors of 714?

Answer: Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714. There are 16 integers that are factors of 714. The greatest factor of 714 is 714.

3. What are the Factors of 722?

Answer: Factors of 722 are 1, 2, 19, 38, 361, 722. There are 6 integers that are factors of 722. The greatest factor of 722 is 722.

4. How to Find the GCF of 714 and 722?

Answer:

Greatest Common Factor of 714 and 722 = 2

Step 1: Find the prime factorization of 714

714 = 2 x 3 x 7 x 17

Step 2: Find the prime factorization of 722

722 = 2 x 19 x 19

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 714 and 722 is 2