Greatest Common Factor of 742 and 749

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 742, 749 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 742 and 749 is 7.

GCF(742,749) = 7

GCF of 742 and 749

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

GCF of:
and

Greatest Common Factor of 742 and 749

GCF of 742 and 749 is 7

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

Prime Factorization of 749


7 749
107 107
1

Prime factors of 749 are 7,107. Prime factorization of 749 in exponential form is:

749 = 71×1071

∴ So by taking common prime factors GCF of 742 and 749 is 7

Greatest Common Factor of 742 and 749 by matching factors method

Factors of 742

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

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

Factors of 749

List of positive integer factors of 749 that divides 749 without a remainder.

1,7,107,749

Greatest Common Factor

We found the factors and prime factorization of 742 and 749. The biggest common factor number is the GCF number.
So the greatest common factor 742 and 749 is 7.

Also check out the Least Common Multiple of 742 and 749

Properties of GCF 742 and 749

(i) The GCF of 742 and 749 is associative

GCF of 742 and 749 = GCF of 749 and 742

Related Greatest Common Factor of 742

Related Greatest Common Factor of 749

Frequently Asked Questions on GCF of 742 and 749

1. What is the GCF of 742 and 749?

Answer: GCF of 742 and 749 is 7.

2. 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.

3. What are the Factors of 749?

Answer: Factors of 749 are 1, 7, 107, 749. There are 4 integers that are factors of 749. The greatest factor of 749 is 749.

4. How to Find the GCF of 742 and 749?

Answer:

Greatest Common Factor of 742 and 749 = 7

Step 1: Find the prime factorization of 742

742 = 2 x 7 x 53

Step 2: Find the prime factorization of 749

749 = 7 x 107

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 742 and 749 is 7