Greatest Common Factor of 105 and 112
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, 112 i.e. 7 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 105 and 112 is 7.
GCF(105,112) = 7
GCF of 105 and 112
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 105 and 112 by prime factorization method
- Greatest Common Factor of 105 and 112 by matching factors method
GCF of 105 and 112 is 7
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 112
| 2 | 112 |
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:
112 = 24×71
∴ So by taking common prime factors GCF of 105 and 112 is 7
Greatest Common Factor of 105 and 112 by matching factors method
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 112
List of positive integer factors of 112 that divides 112 without a remainder.
1,2,4,7,8,14,16,28,56,112
Greatest Common Factor
We found the factors and prime factorization of 105 and 112. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 112 is 7.
Also check out the Least Common Multiple of 105 and 112
Properties of GCF 105 and 112
(i) The GCF of 105 and 112 is associative
GCF of 105 and 112 = GCF of 112 and 105
Related Greatest Common Factor of 105
Related Greatest Common Factor of 112
Frequently Asked Questions on GCF of 105 and 112
1. What is the GCF of 105 and 112?
Answer: GCF of 105 and 112 is 7.
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 112?
Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.
4. How to Find the GCF of 105 and 112?
Answer:
Greatest Common Factor of 105 and 112 = 7
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 112
112 = 2 x 2 x 2 x 2 x 7
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 7
Step 4: Therefore, the greatest common factor of 105 and 112 is 7
