Greatest Common Factor of 726 and 728

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 726, 728 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 726 and 728 is 2.

GCF(726,728) = 2

GCF of 726 and 728

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

GCF of:
and

Greatest Common Factor of 726 and 728

GCF of 726 and 728 is 2

Prime Factorization of 726


2 726
3 363
11 121
11 11
1

Prime factors of 726 are 2,3,11. Prime factorization of 726 in exponential form is:

726 = 21×31×112

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

∴ So by taking common prime factors GCF of 726 and 728 is 2

Greatest Common Factor of 726 and 728 by matching factors method

Factors of 726

List of positive integer factors of 726 that divides 726 without a remainder.

1,2,3,6,11,22,33,66,121,242,363,726

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

Greatest Common Factor

We found the factors and prime factorization of 726 and 728. The biggest common factor number is the GCF number.
So the greatest common factor 726 and 728 is 2.

Also check out the Least Common Multiple of 726 and 728

Properties of GCF 726 and 728

(i) The GCF of 726 and 728 is associative

GCF of 726 and 728 = GCF of 728 and 726

Related Greatest Common Factor of 726

Related Greatest Common Factor of 728

Frequently Asked Questions on GCF of 726 and 728

1. What is the GCF of 726 and 728?

Answer: GCF of 726 and 728 is 2.

2. What are the Factors of 726?

Answer: Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726. There are 12 integers that are factors of 726. The greatest factor of 726 is 726.

3. 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.

4. How to Find the GCF of 726 and 728?

Answer:

Greatest Common Factor of 726 and 728 = 2

Step 1: Find the prime factorization of 726

726 = 2 x 3 x 11 x 11

Step 2: Find the prime factorization of 728

728 = 2 x 2 x 2 x 7 x 13

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 726 and 728 is 2