Greatest Common Factor of 708 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 708, 714 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 708 and 714 is 6.

GCF(708,714) = 6

GCF of 708 and 714

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

GCF of:
and

Greatest Common Factor of 708 and 714

GCF of 708 and 714 is 6

Prime Factorization of 708


2 708
2 354
3 177
59 59
1

Prime factors of 708 are 2,3,59. Prime factorization of 708 in exponential form is:

708 = 22×31×591

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 708 and 714 is 6

Greatest Common Factor of 708 and 714 by matching factors method

Factors of 708

List of positive integer factors of 708 that divides 708 without a remainder.

1,2,3,4,6,12,59,118,177,236,354,708

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 708 and 714. The biggest common factor number is the GCF number.
So the greatest common factor 708 and 714 is 6.

Also check out the Least Common Multiple of 708 and 714

Properties of GCF 708 and 714

(i) The GCF of 708 and 714 is associative

GCF of 708 and 714 = GCF of 714 and 708

Related Greatest Common Factor of 708

Related Greatest Common Factor of 714

Frequently Asked Questions on GCF of 708 and 714

1. What is the GCF of 708 and 714?

Answer: GCF of 708 and 714 is 6.

2. What are the Factors of 708?

Answer: Factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708. There are 12 integers that are factors of 708. The greatest factor of 708 is 708.

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 708 and 714?

Answer:

Greatest Common Factor of 708 and 714 = 6

Step 1: Find the prime factorization of 708

708 = 2 x 2 x 3 x 59

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 x 3 = 6

Step 4: Therefore, the greatest common factor of 708 and 714 is 6