Greatest Common Factor of 700 and 704

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, 704 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 700 and 704 is 4.

GCF(700,704) = 4

GCF of 700 and 704

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

GCF of:
and

Greatest Common Factor of 700 and 704

GCF of 700 and 704 is 4

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 704


2 704
2 352
2 176
2 88
2 44
2 22
11 11
1

Prime factors of 704 are 2,11. Prime factorization of 704 in exponential form is:

704 = 26×111

∴ So by taking common prime factors GCF of 700 and 704 is 4

Greatest Common Factor of 700 and 704 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 704

List of positive integer factors of 704 that divides 704 without a remainder.

1,2,4,8,11,16,22,32,44,64,88,176,352,704

Greatest Common Factor

We found the factors and prime factorization of 700 and 704. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 704 is 4.

Also check out the Least Common Multiple of 700 and 704

Properties of GCF 700 and 704

(i) The GCF of 700 and 704 is associative

GCF of 700 and 704 = GCF of 704 and 700

Related Greatest Common Factor of 700

Related Greatest Common Factor of 704

Frequently Asked Questions on GCF of 700 and 704

1. What is the GCF of 700 and 704?

Answer: GCF of 700 and 704 is 4.

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 704?

Answer: Factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704. There are 14 integers that are factors of 704. The greatest factor of 704 is 704.

4. How to Find the GCF of 700 and 704?

Answer:

Greatest Common Factor of 700 and 704 = 4

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 704

704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 700 and 704 is 4