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 105, 110 i.e. 5 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 105 and 110 is 5.
GCF(105,110) = 5
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 105
3 | 105 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 105 are 3,5,7. Prime factorization of 105 in exponential form is:
105 = 31×51×71
Prime Factorization of 110
2 | 110 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 110 are 2,5,11. Prime factorization of 110 in exponential form is:
110 = 21×51×111
∴ So by taking common prime factors GCF of 105 and 110 is 5
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1,3,5,7,15,21,35,105
Factors of 110
List of positive integer factors of 110 that divides 110 without a remainder.
1,2,5,10,11,22,55,110
Greatest Common Factor
We found the factors and prime factorization of 105 and 110. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 110 is 5.
Also check out the Least Common Multiple of 105 and 110
(i) The GCF of 105 and 110 is associative
GCF of 105 and 110 = GCF of 110 and 105
1. What is the GCF of 105 and 110?
Answer: GCF of 105 and 110 is 5.
2. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
3. What are the Factors of 110?
Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.
4. How to Find the GCF of 105 and 110?
Answer:
Greatest Common Factor of 105 and 110 = 5
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 110
110 = 2 x 5 x 11
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 105 and 110 is 5