Greatest Common Factor of 734 and 742

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 734, 742 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 734 and 742 is 2.

GCF(734,742) = 2

GCF of 734 and 742

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

GCF of:
and

Greatest Common Factor of 734 and 742

GCF of 734 and 742 is 2

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

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 734 and 742 is 2

Greatest Common Factor of 734 and 742 by matching factors method

Factors of 734

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

1,2,367,734

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 734 and 742. The biggest common factor number is the GCF number.
So the greatest common factor 734 and 742 is 2.

Also check out the Least Common Multiple of 734 and 742

Properties of GCF 734 and 742

(i) The GCF of 734 and 742 is associative

GCF of 734 and 742 = GCF of 742 and 734

Related Greatest Common Factor of 734

Related Greatest Common Factor of 742

Frequently Asked Questions on GCF of 734 and 742

1. What is the GCF of 734 and 742?

Answer: GCF of 734 and 742 is 2.

2. 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.

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 734 and 742?

Answer:

Greatest Common Factor of 734 and 742 = 2

Step 1: Find the prime factorization of 734

734 = 2 x 367

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 = 2

Step 4: Therefore, the greatest common factor of 734 and 742 is 2