Greatest Common Factor of 354 and 360

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 354, 360 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 354 and 360 is 6.

GCF(354,360) = 6

GCF of 354 and 360

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

GCF of:
and

Greatest Common Factor of 354 and 360

GCF of 354 and 360 is 6

Prime Factorization of 354


2 354
3 177
59 59
1

Prime factors of 354 are 2,3,59. Prime factorization of 354 in exponential form is:

354 = 21×31×591

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

∴ So by taking common prime factors GCF of 354 and 360 is 6

Greatest Common Factor of 354 and 360 by matching factors method

Factors of 354

List of positive integer factors of 354 that divides 354 without a remainder.

1,2,3,6,59,118,177,354

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

Greatest Common Factor

We found the factors and prime factorization of 354 and 360. The biggest common factor number is the GCF number.
So the greatest common factor 354 and 360 is 6.

Also check out the Least Common Multiple of 354 and 360

Properties of GCF 354 and 360

(i) The GCF of 354 and 360 is associative

GCF of 354 and 360 = GCF of 360 and 354

Related Greatest Common Factor of 354

Related Greatest Common Factor of 360

Frequently Asked Questions on GCF of 354 and 360

1. What is the GCF of 354 and 360?

Answer: GCF of 354 and 360 is 6.

2. What are the Factors of 354?

Answer: Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354. There are 8 integers that are factors of 354. The greatest factor of 354 is 354.

3. 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.

4. How to Find the GCF of 354 and 360?

Answer:

Greatest Common Factor of 354 and 360 = 6

Step 1: Find the prime factorization of 354

354 = 2 x 3 x 59

Step 2: Find the prime factorization of 360

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

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 354 and 360 is 6