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, 186 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 180 and 186 is 6.
GCF(180,186) = 6
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 186
2 | 186 |
3 | 93 |
31 | 31 |
1 |
Prime factors of 186 are 2,3,31. Prime factorization of 186 in exponential form is:
186 = 21×31×311
∴ So by taking common prime factors GCF of 180 and 186 is 6
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 186
List of positive integer factors of 186 that divides 186 without a remainder.
1,2,3,6,31,62,93,186
Greatest Common Factor
We found the factors and prime factorization of 180 and 186. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 186 is 6.
Also check out the Least Common Multiple of 180 and 186
(i) The GCF of 180 and 186 is associative
GCF of 180 and 186 = GCF of 186 and 180
1. What is the GCF of 180 and 186?
Answer: GCF of 180 and 186 is 6.
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 186?
Answer: Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186. There are 8 integers that are factors of 186. The greatest factor of 186 is 186.
4. How to Find the GCF of 180 and 186?
Answer:
Greatest Common Factor of 180 and 186 = 6
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 186
186 = 2 x 3 x 31
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 3 = 6
Step 4: Therefore, the greatest common factor of 180 and 186 is 6