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 1995, 2000 i.e. 5 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1995 and 2000 is 5.
GCF(1995,2000) = 5
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 1995
3 | 1995 |
5 | 665 |
7 | 133 |
19 | 19 |
1 |
Prime factors of 1995 are 3,5,7,19. Prime factorization of 1995 in exponential form is:
1995 = 31×51×71×191
Prime Factorization of 2000
2 | 2000 |
2 | 1000 |
2 | 500 |
2 | 250 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 2000 are 2,5. Prime factorization of 2000 in exponential form is:
2000 = 24×53
∴ So by taking common prime factors GCF of 1995 and 2000 is 5
Factors of 1995
List of positive integer factors of 1995 that divides 1995 without a remainder.
1,3,5,7,15,19,21,35,57,95,105,133,285,399,665,1995
Factors of 2000
List of positive integer factors of 2000 that divides 2000 without a remainder.
1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000
Greatest Common Factor
We found the factors and prime factorization of 1995 and 2000. The biggest common factor number is the GCF number.
So the greatest common factor 1995 and 2000 is 5.
Also check out the Least Common Multiple of 1995 and 2000
(i) The GCF of 1995 and 2000 is associative
GCF of 1995 and 2000 = GCF of 2000 and 1995
1. What is the GCF of 1995 and 2000?
Answer: GCF of 1995 and 2000 is 5.
2. What are the Factors of 1995?
Answer: Factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995. There are 16 integers that are factors of 1995. The greatest factor of 1995 is 1995.
3. What are the Factors of 2000?
Answer: Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. There are 20 integers that are factors of 2000. The greatest factor of 2000 is 2000.
4. How to Find the GCF of 1995 and 2000?
Answer:
Greatest Common Factor of 1995 and 2000 = 5
Step 1: Find the prime factorization of 1995
1995 = 3 x 5 x 7 x 19
Step 2: Find the prime factorization of 2000
2000 = 2 x 2 x 2 x 2 x 5 x 5 x 5
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 1995 and 2000 is 5