Greatest Common Factor of 360 and 364

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 360, 364 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 360 and 364 is 4.

GCF(360,364) = 4

GCF of 360 and 364

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

GCF of:
and

Greatest Common Factor of 360 and 364

GCF of 360 and 364 is 4

Prime Factorization of 360


2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 360 are 2,3,5. Prime factorization of 360 in exponential form is:

360 = 23×32×51

Prime Factorization of 364


2 364
2 182
7 91
13 13
1

Prime factors of 364 are 2,7,13. Prime factorization of 364 in exponential form is:

364 = 22×71×131

∴ So by taking common prime factors GCF of 360 and 364 is 4

Greatest Common Factor of 360 and 364 by matching factors method

Factors of 360

List of positive integer factors of 360 that divides 360 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

Factors of 364

List of positive integer factors of 364 that divides 364 without a remainder.

1,2,4,7,13,14,26,28,52,91,182,364

Greatest Common Factor

We found the factors and prime factorization of 360 and 364. The biggest common factor number is the GCF number.
So the greatest common factor 360 and 364 is 4.

Also check out the Least Common Multiple of 360 and 364

Properties of GCF 360 and 364

(i) The GCF of 360 and 364 is associative

GCF of 360 and 364 = GCF of 364 and 360

Related Greatest Common Factor of 360

Related Greatest Common Factor of 364

Frequently Asked Questions on GCF of 360 and 364

1. What is the GCF of 360 and 364?

Answer: GCF of 360 and 364 is 4.

2. What are the Factors of 360?

Answer: Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. There are 24 integers that are factors of 360. The greatest factor of 360 is 360.

3. What are the Factors of 364?

Answer: Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. There are 12 integers that are factors of 364. The greatest factor of 364 is 364.

4. How to Find the GCF of 360 and 364?

Answer:

Greatest Common Factor of 360 and 364 = 4

Step 1: Find the prime factorization of 360

360 = 2 x 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 364

364 = 2 x 2 x 7 x 13

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 360 and 364 is 4