Greatest Common Factor of 7312 and 7314

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 7312, 7314 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 7312 and 7314 is 2.

GCF(7312,7314) = 2

GCF of 7312 and 7314

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

GCF of:
and

Greatest Common Factor of 7312 and 7314

GCF of 7312 and 7314 is 2

Prime Factorization of 7312


2 7312
2 3656
2 1828
2 914
457 457
1

Prime factors of 7312 are 2,457. Prime factorization of 7312 in exponential form is:

7312 = 24×4571

Prime Factorization of 7314


2 7314
3 3657
23 1219
53 53
1

Prime factors of 7314 are 2,3,23,53. Prime factorization of 7314 in exponential form is:

7314 = 21×31×231×531

∴ So by taking common prime factors GCF of 7312 and 7314 is 2

Greatest Common Factor of 7312 and 7314 by matching factors method

Factors of 7312

List of positive integer factors of 7312 that divides 7312 without a remainder.

1,2,4,8,16,457,914,1828,3656,7312

Factors of 7314

List of positive integer factors of 7314 that divides 7314 without a remainder.

1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314

Greatest Common Factor

We found the factors and prime factorization of 7312 and 7314. The biggest common factor number is the GCF number.
So the greatest common factor 7312 and 7314 is 2.

Also check out the Least Common Multiple of 7312 and 7314

Properties of GCF 7312 and 7314

(i) The GCF of 7312 and 7314 is associative

GCF of 7312 and 7314 = GCF of 7314 and 7312

Related Greatest Common Factor of 7312

Related Greatest Common Factor of 7314

Frequently Asked Questions on GCF of 7312 and 7314

1. What is the GCF of 7312 and 7314?

Answer: GCF of 7312 and 7314 is 2.

2. What are the Factors of 7312?

Answer: Factors of 7312 are 1, 2, 4, 8, 16, 457, 914, 1828, 3656, 7312. There are 10 integers that are factors of 7312. The greatest factor of 7312 is 7312.

3. What are the Factors of 7314?

Answer: Factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314. There are 16 integers that are factors of 7314. The greatest factor of 7314 is 7314.

4. How to Find the GCF of 7312 and 7314?

Answer:

Greatest Common Factor of 7312 and 7314 = 2

Step 1: Find the prime factorization of 7312

7312 = 2 x 2 x 2 x 2 x 457

Step 2: Find the prime factorization of 7314

7314 = 2 x 3 x 23 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 7312 and 7314 is 2