Greatest Common Factor of 180 and 185

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 180, 185 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 180 and 185 is 5.

GCF(180,185) = 5

GCF of 180 and 185

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

GCF of:
and

Greatest Common Factor of 180 and 185

GCF of 180 and 185 is 5

Prime Factorization of 180


2 180
2 90
3 45
3 15
5 5
1

Prime factors of 180 are 2,3,5. Prime factorization of 180 in exponential form is:

180 = 22×32×51

Prime Factorization of 185


5 185
37 37
1

Prime factors of 185 are 5,37. Prime factorization of 185 in exponential form is:

185 = 51×371

∴ So by taking common prime factors GCF of 180 and 185 is 5

Greatest Common Factor of 180 and 185 by matching factors method

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Factors of 185

List of positive integer factors of 185 that divides 185 without a remainder.

1,5,37,185

Greatest Common Factor

We found the factors and prime factorization of 180 and 185. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 185 is 5.

Also check out the Least Common Multiple of 180 and 185

Properties of GCF 180 and 185

(i) The GCF of 180 and 185 is associative

GCF of 180 and 185 = GCF of 185 and 180

Related Greatest Common Factor of 180

Related Greatest Common Factor of 185

Frequently Asked Questions on GCF of 180 and 185

1. What is the GCF of 180 and 185?

Answer: GCF of 180 and 185 is 5.

2. What are the Factors of 180?

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

3. What are the Factors of 185?

Answer: Factors of 185 are 1, 5, 37, 185. There are 4 integers that are factors of 185. The greatest factor of 185 is 185.

4. How to Find the GCF of 180 and 185?

Answer:

Greatest Common Factor of 180 and 185 = 5

Step 1: Find the prime factorization of 180

180 = 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 185

185 = 5 x 37

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

GCF = 5

Step 4: Therefore, the greatest common factor of 180 and 185 is 5