Greatest Common Factor of 754 and 760

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 754, 760 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 754 and 760 is 2.

GCF(754,760) = 2

GCF of 754 and 760

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

GCF of:
and

Greatest Common Factor of 754 and 760

GCF of 754 and 760 is 2

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

Prime Factorization of 760


2 760
2 380
2 190
5 95
19 19
1

Prime factors of 760 are 2,5,19. Prime factorization of 760 in exponential form is:

760 = 23×51×191

∴ So by taking common prime factors GCF of 754 and 760 is 2

Greatest Common Factor of 754 and 760 by matching factors method

Factors of 754

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

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

Factors of 760

List of positive integer factors of 760 that divides 760 without a remainder.

1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760

Greatest Common Factor

We found the factors and prime factorization of 754 and 760. The biggest common factor number is the GCF number.
So the greatest common factor 754 and 760 is 2.

Also check out the Least Common Multiple of 754 and 760

Properties of GCF 754 and 760

(i) The GCF of 754 and 760 is associative

GCF of 754 and 760 = GCF of 760 and 754

Related Greatest Common Factor of 754

Related Greatest Common Factor of 760

Frequently Asked Questions on GCF of 754 and 760

1. What is the GCF of 754 and 760?

Answer: GCF of 754 and 760 is 2.

2. 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.

3. What are the Factors of 760?

Answer: Factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760. There are 16 integers that are factors of 760. The greatest factor of 760 is 760.

4. How to Find the GCF of 754 and 760?

Answer:

Greatest Common Factor of 754 and 760 = 2

Step 1: Find the prime factorization of 754

754 = 2 x 13 x 29

Step 2: Find the prime factorization of 760

760 = 2 x 2 x 2 x 5 x 19

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 754 and 760 is 2