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Greatest Common Factor of 735 and 742

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 735, 742 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 735 and 742 is 7.

GCF(735,742) = 7

GCF of 735 and 742

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

GCF of:
and

Greatest Common Factor of 735 and 742 by Prime factorization method

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 742


2 742
7 371
53 53
1

Prime factors of 742 are 2,7,53. Prime factorization of 742 in exponential form is:

742 = 21×71×531

∴ So by taking common prime factors GCF of 735 and 742 is 7

Greatest Common Factor of 735 and 742 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 742

List of positive integer factors of 742 that divides 742 without a remainder.

1,2,7,14,53,106,371,742

Greatest Common Factor

We found the factors and prime factorization of 735 and 742. The biggest common factor number is the GCF number.
So the greatest common factor 735 and 742 is 7.

Also check out the Least Common Multiple of 735 and 742

Properties of GCF 735 and 742

(i) The GCF of 735 and 742 is associative

GCF of 735 and 742 = GCF of 742 and 735

Frequently Asked Questions on GCF of 735 and 742

1. What is the GCF of 735 and 742?

Answer: GCF of 735 and 742 is 7.

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 742?

Answer: Factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742. There are 8 integers that are factors of 742. The greatest factor of 742 is 742.

4. How to Find the GCF of 735 and 742?

Answer:

Greatest Common Factor of 735 and 742 = 7

Step 1: Find the prime factorization of 735

735 = 3 x 5 x 7 x 7

Step 2: Find the prime factorization of 742

742 = 2 x 7 x 53

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

GCF = 7

Step 4: Therefore, the greatest common factor of 735 and 742 is 7