Greatest Common Factor of 728 and 735

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 728, 735 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 728 and 735 is 7.

GCF(728,735) = 7

GCF of 728 and 735

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

GCF of:
and

Greatest Common Factor of 728 and 735

GCF of 728 and 735 is 7

Prime Factorization of 728


2 728
2 364
2 182
7 91
13 13
1

Prime factors of 728 are 2,7,13. Prime factorization of 728 in exponential form is:

728 = 23×71×131

Prime Factorization of 735


3 735
5 245
7 49
7 7
1

Prime factors of 735 are 3,5,7. Prime factorization of 735 in exponential form is:

735 = 31×51×72

∴ So by taking common prime factors GCF of 728 and 735 is 7

Greatest Common Factor of 728 and 735 by matching factors method

Factors of 728

List of positive integer factors of 728 that divides 728 without a remainder.

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1,3,5,7,15,21,35,49,105,147,245,735

Greatest Common Factor

We found the factors and prime factorization of 728 and 735. The biggest common factor number is the GCF number.
So the greatest common factor 728 and 735 is 7.

Also check out the Least Common Multiple of 728 and 735

Properties of GCF 728 and 735

(i) The GCF of 728 and 735 is associative

GCF of 728 and 735 = GCF of 735 and 728

Related Greatest Common Factor of 728

Related Greatest Common Factor of 735

Frequently Asked Questions on GCF of 728 and 735

1. What is the GCF of 728 and 735?

Answer: GCF of 728 and 735 is 7.

2. What are the Factors of 728?

Answer: Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. There are 16 integers that are factors of 728. The greatest factor of 728 is 728.

3. What are the Factors of 735?

Answer: Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. There are 12 integers that are factors of 735. The greatest factor of 735 is 735.

4. How to Find the GCF of 728 and 735?

Answer:

Greatest Common Factor of 728 and 735 = 7

Step 1: Find the prime factorization of 728

728 = 2 x 2 x 2 x 7 x 13

Step 2: Find the prime factorization of 735

735 = 3 x 5 x 7 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 728 and 735 is 7