Greatest Common Factor of 700 and 706

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 700, 706 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 700 and 706 is 2.

GCF(700,706) = 2

GCF of 700 and 706

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

GCF of:
and

Greatest Common Factor of 700 and 706

GCF of 700 and 706 is 2

Prime Factorization of 700


2 700
2 350
5 175
5 35
7 7
1

Prime factors of 700 are 2,5,7. Prime factorization of 700 in exponential form is:

700 = 22×52×71

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

∴ So by taking common prime factors GCF of 700 and 706 is 2

Greatest Common Factor of 700 and 706 by matching factors method

Factors of 700

List of positive integer factors of 700 that divides 700 without a remainder.

1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700

Factors of 706

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

1,2,353,706

Greatest Common Factor

We found the factors and prime factorization of 700 and 706. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 706 is 2.

Also check out the Least Common Multiple of 700 and 706

Properties of GCF 700 and 706

(i) The GCF of 700 and 706 is associative

GCF of 700 and 706 = GCF of 706 and 700

Related Greatest Common Factor of 700

Related Greatest Common Factor of 706

Frequently Asked Questions on GCF of 700 and 706

1. What is the GCF of 700 and 706?

Answer: GCF of 700 and 706 is 2.

2. What are the Factors of 700?

Answer: Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700. There are 18 integers that are factors of 700. The greatest factor of 700 is 700.

3. 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.

4. How to Find the GCF of 700 and 706?

Answer:

Greatest Common Factor of 700 and 706 = 2

Step 1: Find the prime factorization of 700

700 = 2 x 2 x 5 x 5 x 7

Step 2: Find the prime factorization of 706

706 = 2 x 353

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 700 and 706 is 2