Greatest Common Factor of 175 and 180

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 175, 180 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 175 and 180 is 5.

GCF(175,180) = 5

GCF of 175 and 180

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

GCF of:
and

Greatest Common Factor of 175 and 180

GCF of 175 and 180 is 5

Prime Factorization of 175


5 175
5 35
7 7
1

Prime factors of 175 are 5,7. Prime factorization of 175 in exponential form is:

175 = 52×71

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

∴ So by taking common prime factors GCF of 175 and 180 is 5

Greatest Common Factor of 175 and 180 by matching factors method

Factors of 175

List of positive integer factors of 175 that divides 175 without a remainder.

1,5,7,25,35,175

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

Greatest Common Factor

We found the factors and prime factorization of 175 and 180. The biggest common factor number is the GCF number.
So the greatest common factor 175 and 180 is 5.

Also check out the Least Common Multiple of 175 and 180

Properties of GCF 175 and 180

(i) The GCF of 175 and 180 is associative

GCF of 175 and 180 = GCF of 180 and 175

Related Greatest Common Factor of 175

Related Greatest Common Factor of 180

Frequently Asked Questions on GCF of 175 and 180

1. What is the GCF of 175 and 180?

Answer: GCF of 175 and 180 is 5.

2. What are the Factors of 175?

Answer: Factors of 175 are 1, 5, 7, 25, 35, 175. There are 6 integers that are factors of 175. The greatest factor of 175 is 175.

3. 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.

4. How to Find the GCF of 175 and 180?

Answer:

Greatest Common Factor of 175 and 180 = 5

Step 1: Find the prime factorization of 175

175 = 5 x 5 x 7

Step 2: Find the prime factorization of 180

180 = 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 = 5

Step 4: Therefore, the greatest common factor of 175 and 180 is 5