Greatest Common Factor of 700 and 705

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, 705 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 700 and 705 is 5.

GCF(700,705) = 5

GCF of 700 and 705

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

GCF of:
and

Greatest Common Factor of 700 and 705

GCF of 700 and 705 is 5

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 705


3 705
5 235
47 47
1

Prime factors of 705 are 3,5,47. Prime factorization of 705 in exponential form is:

705 = 31×51×471

∴ So by taking common prime factors GCF of 700 and 705 is 5

Greatest Common Factor of 700 and 705 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 705

List of positive integer factors of 705 that divides 705 without a remainder.

1,3,5,15,47,141,235,705

Greatest Common Factor

We found the factors and prime factorization of 700 and 705. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 705 is 5.

Also check out the Least Common Multiple of 700 and 705

Properties of GCF 700 and 705

(i) The GCF of 700 and 705 is associative

GCF of 700 and 705 = GCF of 705 and 700

Related Greatest Common Factor of 700

Related Greatest Common Factor of 705

Frequently Asked Questions on GCF of 700 and 705

1. What is the GCF of 700 and 705?

Answer: GCF of 700 and 705 is 5.

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 705?

Answer: Factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705. There are 8 integers that are factors of 705. The greatest factor of 705 is 705.

4. How to Find the GCF of 700 and 705?

Answer:

Greatest Common Factor of 700 and 705 = 5

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 705

705 = 3 x 5 x 47

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

GCF = 5

Step 4: Therefore, the greatest common factor of 700 and 705 is 5