Greatest Common Factor of 749 and 754

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 749, 754 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 749 and 754 is 1.

GCF(749,754) = 1

GCF of 749 and 754

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

GCF of:
and

Greatest Common Factor of 749 and 754

GCF of 749 and 754 is 1

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

Prime Factorization of 754


2 754
13 377
29 29
1

Prime factors of 754 are 2,13,29. Prime factorization of 754 in exponential form is:

754 = 21×131×291

∴ So by taking common prime factors GCF of 749 and 754 is 1

Greatest Common Factor of 749 and 754 by matching factors method

Factors of 749

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

1,7,107,749

Factors of 754

List of positive integer factors of 754 that divides 754 without a remainder.

1,2,13,26,29,58,377,754

Greatest Common Factor

We found the factors and prime factorization of 749 and 754. The biggest common factor number is the GCF number.
So the greatest common factor 749 and 754 is 1.

Also check out the Least Common Multiple of 749 and 754

Properties of GCF 749 and 754

(i) The GCF of 749 and 754 is associative

GCF of 749 and 754 = GCF of 754 and 749

Related Greatest Common Factor of 749

Related Greatest Common Factor of 754

Frequently Asked Questions on GCF of 749 and 754

1. What is the GCF of 749 and 754?

Answer: GCF of 749 and 754 is 1.

2. 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.

3. What are the Factors of 754?

Answer: Factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754. There are 8 integers that are factors of 754. The greatest factor of 754 is 754.

4. How to Find the GCF of 749 and 754?

Answer:

Greatest Common Factor of 749 and 754 = 1

Step 1: Find the prime factorization of 749

749 = 7 x 107

Step 2: Find the prime factorization of 754

754 = 2 x 13 x 29

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 749 and 754 is 1