# Greatest Common Factor of 176 and 180

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 176, 180 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 176 and 180 is 4.

GCF(176,180) = 4

## GCF of 176 and 180

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

GCF of:
and

### Greatest Common Factor of 176 and 180 by Prime factorization method

Prime Factorization of 176

 2 176 2 88 2 44 2 22 11 11 1

Prime factors of 176 are 2,11. Prime factorization of 176 in exponential form is:

176 = 24×111

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 176 and 180 is 4

### Greatest Common Factor of 176 and 180 by matching factors method

Factors of 176

List of positive integer factors of 176 that divides 176 without a remainder.

1,2,4,8,11,16,22,44,88,176

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 176 and 180. The biggest common factor number is the GCF number.
So the greatest common factor 176 and 180 is 4.

Also check out the Least Common Multiple of 176 and 180

### Properties of GCF 176 and 180

(i) The GCF of 176 and 180 is associative

GCF of 176 and 180 = GCF of 180 and 176

### Frequently Asked Questions on GCF of 176 and 180

1. What is the GCF of 176 and 180?

Answer: GCF of 176 and 180 is 4.

2. What are the Factors of 176?

Answer: Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. There are 10 integers that are factors of 176. The greatest factor of 176 is 176.

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 176 and 180?

Greatest Common Factor of 176 and 180 = 4

Step 1: Find the prime factorization of 176

176 = 2 x 2 x 2 x 2 x 11

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 = 4

Step 4: Therefore, the greatest common factor of 176 and 180 is 4