# Greatest Common Factor of 728 and 734

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 728, 734 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 728 and 734 is 2.

GCF(728,734) = 2

## GCF of 728 and 734

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

GCF of:
and

### Greatest Common Factor of 728 and 734 by Prime factorization method

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 734

 2 734 367 367 1

Prime factors of 734 are 2,367. Prime factorization of 734 in exponential form is:

734 = 21×3671

∴ So by taking common prime factors GCF of 728 and 734 is 2

### Greatest Common Factor of 728 and 734 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 734

List of positive integer factors of 734 that divides 734 without a remainder.

1,2,367,734

Greatest Common Factor

We found the factors and prime factorization of 728 and 734. The biggest common factor number is the GCF number.
So the greatest common factor 728 and 734 is 2.

Also check out the Least Common Multiple of 728 and 734

### Properties of GCF 728 and 734

(i) The GCF of 728 and 734 is associative

GCF of 728 and 734 = GCF of 734 and 728

### Frequently Asked Questions on GCF of 728 and 734

1. What is the GCF of 728 and 734?

Answer: GCF of 728 and 734 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 734?

Answer: Factors of 734 are 1, 2, 367, 734. There are 4 integers that are factors of 734. The greatest factor of 734 is 734.

4. How to Find the GCF of 728 and 734?

Greatest Common Factor of 728 and 734 = 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 734

734 = 2 x 367

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 734 is 2