Greatest Common Factor of 746 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 746, 754 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 746 and 754 is 2.

GCF(746,754) = 2

GCF of 746 and 754

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

GCF of:
and

Greatest Common Factor of 746 and 754

GCF of 746 and 754 is 2

Prime Factorization of 746


2 746
373 373
1

Prime factors of 746 are 2,373. Prime factorization of 746 in exponential form is:

746 = 21×3731

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 746 and 754 is 2

Greatest Common Factor of 746 and 754 by matching factors method

Factors of 746

List of positive integer factors of 746 that divides 746 without a remainder.

1,2,373,746

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 746 and 754. The biggest common factor number is the GCF number.
So the greatest common factor 746 and 754 is 2.

Also check out the Least Common Multiple of 746 and 754

Properties of GCF 746 and 754

(i) The GCF of 746 and 754 is associative

GCF of 746 and 754 = GCF of 754 and 746

Related Greatest Common Factor of 746

Related Greatest Common Factor of 754

Frequently Asked Questions on GCF of 746 and 754

1. What is the GCF of 746 and 754?

Answer: GCF of 746 and 754 is 2.

2. What are the Factors of 746?

Answer: Factors of 746 are 1, 2, 373, 746. There are 4 integers that are factors of 746. The greatest factor of 746 is 746.

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 746 and 754?

Answer:

Greatest Common Factor of 746 and 754 = 2

Step 1: Find the prime factorization of 746

746 = 2 x 373

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 = 2

Step 4: Therefore, the greatest common factor of 746 and 754 is 2