Greatest Common Factor of 728 and 730

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

Greatest common factor (GCF) of 728 and 730 is 2.

GCF(728,730) = 2

GCF of 728 and 730

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

GCF of:
and

Greatest Common Factor of 728 and 730

GCF of 728 and 730 is 2

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 730


2 730
5 365
73 73
1

Prime factors of 730 are 2,5,73. Prime factorization of 730 in exponential form is:

730 = 21×51×731

∴ So by taking common prime factors GCF of 728 and 730 is 2

Greatest Common Factor of 728 and 730 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 730

List of positive integer factors of 730 that divides 730 without a remainder.

1,2,5,10,73,146,365,730

Greatest Common Factor

We found the factors and prime factorization of 728 and 730. The biggest common factor number is the GCF number.
So the greatest common factor 728 and 730 is 2.

Also check out the Least Common Multiple of 728 and 730

Properties of GCF 728 and 730

(i) The GCF of 728 and 730 is associative

GCF of 728 and 730 = GCF of 730 and 728

Related Greatest Common Factor of 728

Related Greatest Common Factor of 730

Frequently Asked Questions on GCF of 728 and 730

1. What is the GCF of 728 and 730?

Answer: GCF of 728 and 730 is 2.

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 730?

Answer: Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730. There are 8 integers that are factors of 730. The greatest factor of 730 is 730.

4. How to Find the GCF of 728 and 730?

Answer:

Greatest Common Factor of 728 and 730 = 2

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 730

730 = 2 x 5 x 73

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 728 and 730 is 2