Greatest Common Factor of 714 and 721

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

Greatest common factor (GCF) of 714 and 721 is 7.

GCF(714,721) = 7

GCF of 714 and 721

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

GCF of:
and

Greatest Common Factor of 714 and 721

GCF of 714 and 721 is 7

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 721


7 721
103 103
1

Prime factors of 721 are 7,103. Prime factorization of 721 in exponential form is:

721 = 71×1031

∴ So by taking common prime factors GCF of 714 and 721 is 7

Greatest Common Factor of 714 and 721 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 721

List of positive integer factors of 721 that divides 721 without a remainder.

1,7,103,721

Greatest Common Factor

We found the factors and prime factorization of 714 and 721. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 721 is 7.

Also check out the Least Common Multiple of 714 and 721

Properties of GCF 714 and 721

(i) The GCF of 714 and 721 is associative

GCF of 714 and 721 = GCF of 721 and 714

Related Greatest Common Factor of 714

Related Greatest Common Factor of 721

Frequently Asked Questions on GCF of 714 and 721

1. What is the GCF of 714 and 721?

Answer: GCF of 714 and 721 is 7.

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 721?

Answer: Factors of 721 are 1, 7, 103, 721. There are 4 integers that are factors of 721. The greatest factor of 721 is 721.

4. How to Find the GCF of 714 and 721?

Answer:

Greatest Common Factor of 714 and 721 = 7

Step 1: Find the prime factorization of 714

714 = 2 x 3 x 7 x 17

Step 2: Find the prime factorization of 721

721 = 7 x 103

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 714 and 721 is 7