Greatest Common Factor of 735 and 738

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 735, 738 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 735 and 738 is 3.

GCF(735,738) = 3

GCF of 735 and 738

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

GCF of:
and

Greatest Common Factor of 735 and 738

GCF of 735 and 738 is 3

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

Prime Factorization of 738


2 738
3 369
3 123
41 41
1

Prime factors of 738 are 2,3,41. Prime factorization of 738 in exponential form is:

738 = 21×32×411

∴ So by taking common prime factors GCF of 735 and 738 is 3

Greatest Common Factor of 735 and 738 by matching factors method

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

Factors of 738

List of positive integer factors of 738 that divides 738 without a remainder.

1,2,3,6,9,18,41,82,123,246,369,738

Greatest Common Factor

We found the factors and prime factorization of 735 and 738. The biggest common factor number is the GCF number.
So the greatest common factor 735 and 738 is 3.

Also check out the Least Common Multiple of 735 and 738

Properties of GCF 735 and 738

(i) The GCF of 735 and 738 is associative

GCF of 735 and 738 = GCF of 738 and 735

Related Greatest Common Factor of 735

Related Greatest Common Factor of 738

Frequently Asked Questions on GCF of 735 and 738

1. What is the GCF of 735 and 738?

Answer: GCF of 735 and 738 is 3.

2. 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.

3. What are the Factors of 738?

Answer: Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738. There are 12 integers that are factors of 738. The greatest factor of 738 is 738.

4. How to Find the GCF of 735 and 738?

Answer:

Greatest Common Factor of 735 and 738 = 3

Step 1: Find the prime factorization of 735

735 = 3 x 5 x 7 x 7

Step 2: Find the prime factorization of 738

738 = 2 x 3 x 3 x 41

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 735 and 738 is 3