Greatest Common Factor of 100 and 105
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 100, 105 i.e. 5 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 100 and 105 is 5.
GCF(100,105) = 5
GCF of 100 and 105
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 100 and 105 by prime factorization method
- Greatest Common Factor of 100 and 105 by matching factors method
GCF of 100 and 105 is 5
Prime Factorization of 100
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:
100 = 22×52
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
∴ So by taking common prime factors GCF of 100 and 105 is 5
Greatest Common Factor of 100 and 105 by matching factors method
Factors of 100
List of positive integer factors of 100 that divides 100 without a remainder.
1,2,4,5,10,20,25,50,100
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors and prime factorization of 100 and 105. The biggest common factor number is the GCF number.
So the greatest common factor 100 and 105 is 5.
Also check out the Least Common Multiple of 100 and 105
Properties of GCF 100 and 105
(i) The GCF of 100 and 105 is associative
GCF of 100 and 105 = GCF of 105 and 100
Related Greatest Common Factor of 100
Related Greatest Common Factor of 105
Frequently Asked Questions on GCF of 100 and 105
1. What is the GCF of 100 and 105?
Answer: GCF of 100 and 105 is 5.
2. What are the Factors of 100?
Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.
3. 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.
4. How to Find the GCF of 100 and 105?
Answer:
Greatest Common Factor of 100 and 105 = 5
Step 1: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 105
105 = 3 x 5 x 7
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 100 and 105 is 5