Greatest Common Factor of 105 and 106
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, 106 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 105 and 106 is 1.
GCF(105,106) = 1
GCF of 105 and 106
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 105 and 106 by prime factorization method
- Greatest Common Factor of 105 and 106 by matching factors method
GCF of 105 and 106 is 1
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 106
| 2 | 106 |
| 53 | 53 |
| 1 |
Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:
106 = 21×531
∴ So by taking common prime factors GCF of 105 and 106 is 1
Greatest Common Factor of 105 and 106 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 106
List of positive integer factors of 106 that divides 106 without a remainder.
1,2,53,106
Greatest Common Factor
We found the factors and prime factorization of 105 and 106. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 106 is 1.
Also check out the Least Common Multiple of 105 and 106
Properties of GCF 105 and 106
(i) The GCF of 105 and 106 is associative
GCF of 105 and 106 = GCF of 106 and 105
Related Greatest Common Factor of 105
Related Greatest Common Factor of 106
Frequently Asked Questions on GCF of 105 and 106
1. What is the GCF of 105 and 106?
Answer: GCF of 105 and 106 is 1.
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 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
4. How to Find the GCF of 105 and 106?
Answer:
Greatest Common Factor of 105 and 106 = 1
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 106
106 = 2 x 53
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = = 1
Step 4: Therefore, the greatest common factor of 105 and 106 is 1
