Greatest Common Factor of 180 and 190

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, 190 i.e. 10 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 180 and 190 is 10.

GCF(180,190) = 10

GCF of 180 and 190

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

GCF of:
and

Greatest Common Factor of 180 and 190

GCF of 180 and 190 is 10

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 190


2 190
5 95
19 19
1

Prime factors of 190 are 2,5,19. Prime factorization of 190 in exponential form is:

190 = 21×51×191

∴ So by taking common prime factors GCF of 180 and 190 is 10

Greatest Common Factor of 180 and 190 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 190

List of positive integer factors of 190 that divides 190 without a remainder.

1,2,5,10,19,38,95,190

Greatest Common Factor

We found the factors and prime factorization of 180 and 190. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 190 is 10.

Also check out the Least Common Multiple of 180 and 190

Properties of GCF 180 and 190

(i) The GCF of 180 and 190 is associative

GCF of 180 and 190 = GCF of 190 and 180

Related Greatest Common Factor of 180

Related Greatest Common Factor of 190

Frequently Asked Questions on GCF of 180 and 190

1. What is the GCF of 180 and 190?

Answer: GCF of 180 and 190 is 10.

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 190?

Answer: Factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190. There are 8 integers that are factors of 190. The greatest factor of 190 is 190.

4. How to Find the GCF of 180 and 190?

Answer:

Greatest Common Factor of 180 and 190 = 10

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 190

190 = 2 x 5 x 19

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

GCF = 2 x 5 = 10

Step 4: Therefore, the greatest common factor of 180 and 190 is 10