Greatest Common Factor of 707 and 714

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 707, 714 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 707 and 714 is 7.

GCF(707,714) = 7

GCF of 707 and 714

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

GCF of:
and

Greatest Common Factor of 707 and 714

GCF of 707 and 714 is 7

Prime Factorization of 707


7 707
101 101
1

Prime factors of 707 are 7,101. Prime factorization of 707 in exponential form is:

707 = 71×1011

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

∴ So by taking common prime factors GCF of 707 and 714 is 7

Greatest Common Factor of 707 and 714 by matching factors method

Factors of 707

List of positive integer factors of 707 that divides 707 without a remainder.

1,7,101,707

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

Greatest Common Factor

We found the factors and prime factorization of 707 and 714. The biggest common factor number is the GCF number.
So the greatest common factor 707 and 714 is 7.

Also check out the Least Common Multiple of 707 and 714

Properties of GCF 707 and 714

(i) The GCF of 707 and 714 is associative

GCF of 707 and 714 = GCF of 714 and 707

Related Greatest Common Factor of 707

Related Greatest Common Factor of 714

Frequently Asked Questions on GCF of 707 and 714

1. What is the GCF of 707 and 714?

Answer: GCF of 707 and 714 is 7.

2. What are the Factors of 707?

Answer: Factors of 707 are 1, 7, 101, 707. There are 4 integers that are factors of 707. The greatest factor of 707 is 707.

3. 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.

4. How to Find the GCF of 707 and 714?

Answer:

Greatest Common Factor of 707 and 714 = 7

Step 1: Find the prime factorization of 707

707 = 7 x 101

Step 2: Find the prime factorization of 714

714 = 2 x 3 x 7 x 17

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 707 and 714 is 7