Greatest Common Factor of 160 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 160, 180 i.e. 20 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 160 and 180 is 20.

GCF(160,180) = 20

GCF of 160 and 180

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

GCF of:
and

Greatest Common Factor of 160 and 180

GCF of 160 and 180 is 20

Prime Factorization of 160


2 160
2 80
2 40
2 20
2 10
5 5
1

Prime factors of 160 are 2,5. Prime factorization of 160 in exponential form is:

160 = 25×51

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 160 and 180 is 20

Greatest Common Factor of 160 and 180 by matching factors method

Factors of 160

List of positive integer factors of 160 that divides 160 without a remainder.

1,2,4,5,8,10,16,20,32,40,80,160

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 160 and 180. The biggest common factor number is the GCF number.
So the greatest common factor 160 and 180 is 20.

Also check out the Least Common Multiple of 160 and 180

Properties of GCF 160 and 180

(i) The GCF of 160 and 180 is associative

GCF of 160 and 180 = GCF of 180 and 160

Frequently Asked Questions on GCF of 160 and 180

1. What is the GCF of 160 and 180?

Answer: GCF of 160 and 180 is 20.

2. What are the Factors of 160?

Answer: Factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. There are 12 integers that are factors of 160. The greatest factor of 160 is 160.

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 160 and 180?

Answer:

Greatest Common Factor of 160 and 180 = 20

Step 1: Find the prime factorization of 160

160 = 2 x 2 x 2 x 2 x 2 x 5

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 = 2 x 2 x 5 = 20

Step 4: Therefore, the greatest common factor of 160 and 180 is 20