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, 185 i.e. 5 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 180 and 185 is 5.
GCF(180,185) = 5
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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 185
5 | 185 |
37 | 37 |
1 |
Prime factors of 185 are 5,37. Prime factorization of 185 in exponential form is:
185 = 51×371
∴ So by taking common prime factors GCF of 180 and 185 is 5
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 185
List of positive integer factors of 185 that divides 185 without a remainder.
1,5,37,185
Greatest Common Factor
We found the factors and prime factorization of 180 and 185. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 185 is 5.
Also check out the Least Common Multiple of 180 and 185
(i) The GCF of 180 and 185 is associative
GCF of 180 and 185 = GCF of 185 and 180
1. What is the GCF of 180 and 185?
Answer: GCF of 180 and 185 is 5.
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 185?
Answer: Factors of 185 are 1, 5, 37, 185. There are 4 integers that are factors of 185. The greatest factor of 185 is 185.
4. How to Find the GCF of 180 and 185?
Answer:
Greatest Common Factor of 180 and 185 = 5
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 185
185 = 5 x 37
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 180 and 185 is 5