Greatest Common Factor of 693 and 700

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 693, 700 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 693 and 700 is 7.

GCF(693,700) = 7

GCF of 693 and 700

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

GCF of:
and

Greatest Common Factor of 693 and 700

GCF of 693 and 700 is 7

Prime Factorization of 693


3 693
3 231
7 77
11 11
1

Prime factors of 693 are 3,7,11. Prime factorization of 693 in exponential form is:

693 = 32×71×111

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

∴ So by taking common prime factors GCF of 693 and 700 is 7

Greatest Common Factor of 693 and 700 by matching factors method

Factors of 693

List of positive integer factors of 693 that divides 693 without a remainder.

1,3,7,9,11,21,33,63,77,99,231,693

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

Greatest Common Factor

We found the factors and prime factorization of 693 and 700. The biggest common factor number is the GCF number.
So the greatest common factor 693 and 700 is 7.

Also check out the Least Common Multiple of 693 and 700

Properties of GCF 693 and 700

(i) The GCF of 693 and 700 is associative

GCF of 693 and 700 = GCF of 700 and 693

Related Greatest Common Factor of 693

Related Greatest Common Factor of 700

Frequently Asked Questions on GCF of 693 and 700

1. What is the GCF of 693 and 700?

Answer: GCF of 693 and 700 is 7.

2. What are the Factors of 693?

Answer: Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693. There are 12 integers that are factors of 693. The greatest factor of 693 is 693.

3. 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.

4. How to Find the GCF of 693 and 700?

Answer:

Greatest Common Factor of 693 and 700 = 7

Step 1: Find the prime factorization of 693

693 = 3 x 3 x 7 x 11

Step 2: Find the prime factorization of 700

700 = 2 x 2 x 5 x 5 x 7

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

GCF = 7

Step 4: Therefore, the greatest common factor of 693 and 700 is 7