Greatest Common Factor of 714 and 717

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, 717 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 714 and 717 is 3.

GCF(714,717) = 3

GCF of 714 and 717

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

GCF of:
and

Greatest Common Factor of 714 and 717

GCF of 714 and 717 is 3

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 717


3 717
239 239
1

Prime factors of 717 are 3,239. Prime factorization of 717 in exponential form is:

717 = 31×2391

∴ So by taking common prime factors GCF of 714 and 717 is 3

Greatest Common Factor of 714 and 717 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 717

List of positive integer factors of 717 that divides 717 without a remainder.

1,3,239,717

Greatest Common Factor

We found the factors and prime factorization of 714 and 717. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 717 is 3.

Also check out the Least Common Multiple of 714 and 717

Properties of GCF 714 and 717

(i) The GCF of 714 and 717 is associative

GCF of 714 and 717 = GCF of 717 and 714

Related Greatest Common Factor of 714

Related Greatest Common Factor of 717

Frequently Asked Questions on GCF of 714 and 717

1. What is the GCF of 714 and 717?

Answer: GCF of 714 and 717 is 3.

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 717?

Answer: Factors of 717 are 1, 3, 239, 717. There are 4 integers that are factors of 717. The greatest factor of 717 is 717.

4. How to Find the GCF of 714 and 717?

Answer:

Greatest Common Factor of 714 and 717 = 3

Step 1: Find the prime factorization of 714

714 = 2 x 3 x 7 x 17

Step 2: Find the prime factorization of 717

717 = 3 x 239

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

GCF = 3

Step 4: Therefore, the greatest common factor of 714 and 717 is 3