Greatest Common Factor of 706 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 706, 714 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 706 and 714 is 2.

GCF(706,714) = 2

GCF of 706 and 714

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

GCF of:
and

Greatest Common Factor of 706 and 714

GCF of 706 and 714 is 2

Prime Factorization of 706


2 706
353 353
1

Prime factors of 706 are 2,353. Prime factorization of 706 in exponential form is:

706 = 21×3531

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 706 and 714 is 2

Greatest Common Factor of 706 and 714 by matching factors method

Factors of 706

List of positive integer factors of 706 that divides 706 without a remainder.

1,2,353,706

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 706 and 714. The biggest common factor number is the GCF number.
So the greatest common factor 706 and 714 is 2.

Also check out the Least Common Multiple of 706 and 714

Properties of GCF 706 and 714

(i) The GCF of 706 and 714 is associative

GCF of 706 and 714 = GCF of 714 and 706

Related Greatest Common Factor of 706

Related Greatest Common Factor of 714

Frequently Asked Questions on GCF of 706 and 714

1. What is the GCF of 706 and 714?

Answer: GCF of 706 and 714 is 2.

2. What are the Factors of 706?

Answer: Factors of 706 are 1, 2, 353, 706. There are 4 integers that are factors of 706. The greatest factor of 706 is 706.

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 706 and 714?

Answer:

Greatest Common Factor of 706 and 714 = 2

Step 1: Find the prime factorization of 706

706 = 2 x 353

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 = 2

Step 4: Therefore, the greatest common factor of 706 and 714 is 2