Greatest Common Factor of 722 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 722, 728 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 722 and 728 is 2.

GCF(722,728) = 2

GCF of 722 and 728

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

GCF of:
and

Greatest Common Factor of 722 and 728

GCF of 722 and 728 is 2

Prime Factorization of 722


2 722
19 361
19 19
1

Prime factors of 722 are 2,19. Prime factorization of 722 in exponential form is:

722 = 21×192

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 722 and 728 is 2

Greatest Common Factor of 722 and 728 by matching factors method

Factors of 722

List of positive integer factors of 722 that divides 722 without a remainder.

1,2,19,38,361,722

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 722 and 728. The biggest common factor number is the GCF number.
So the greatest common factor 722 and 728 is 2.

Also check out the Least Common Multiple of 722 and 728

Properties of GCF 722 and 728

(i) The GCF of 722 and 728 is associative

GCF of 722 and 728 = GCF of 728 and 722

Related Greatest Common Factor of 722

Related Greatest Common Factor of 728

Frequently Asked Questions on GCF of 722 and 728

1. What is the GCF of 722 and 728?

Answer: GCF of 722 and 728 is 2.

2. What are the Factors of 722?

Answer: Factors of 722 are 1, 2, 19, 38, 361, 722. There are 6 integers that are factors of 722. The greatest factor of 722 is 722.

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 722 and 728?

Answer:

Greatest Common Factor of 722 and 728 = 2

Step 1: Find the prime factorization of 722

722 = 2 x 19 x 19

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 722 and 728 is 2