Greatest Common Factor of 180 and 200

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, 200 i.e. 20 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 180 and 200 is 20.

GCF(180,200) = 20

GCF of 180 and 200

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

GCF of:
and

Greatest Common Factor of 180 and 200

GCF of 180 and 200 is 20

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 200


2 200
2 100
2 50
5 25
5 5
1

Prime factors of 200 are 2,5. Prime factorization of 200 in exponential form is:

200 = 23×52

∴ So by taking common prime factors GCF of 180 and 200 is 20

Greatest Common Factor of 180 and 200 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 200

List of positive integer factors of 200 that divides 200 without a remainder.

1,2,4,5,8,10,20,25,40,50,100,200

Greatest Common Factor

We found the factors and prime factorization of 180 and 200. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 200 is 20.

Also check out the Least Common Multiple of 180 and 200

Properties of GCF 180 and 200

(i) The GCF of 180 and 200 is associative

GCF of 180 and 200 = GCF of 200 and 180

Related Greatest Common Factor of 180

Related Greatest Common Factor of 200

Frequently Asked Questions on GCF of 180 and 200

1. What is the GCF of 180 and 200?

Answer: GCF of 180 and 200 is 20.

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 200?

Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.

4. How to Find the GCF of 180 and 200?

Answer:

Greatest Common Factor of 180 and 200 = 20

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 200

200 = 2 x 2 x 2 x 5 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 2 x 5 = 20

Step 4: Therefore, the greatest common factor of 180 and 200 is 20