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 1000, 1004 i.e. 4 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1000 and 1004 is 4.
GCF(1000,1004) = 4
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 1000
2 | 1000 |
2 | 500 |
2 | 250 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 1000 are 2,5. Prime factorization of 1000 in exponential form is:
1000 = 23×53
Prime Factorization of 1004
2 | 1004 |
2 | 502 |
251 | 251 |
1 |
Prime factors of 1004 are 2,251. Prime factorization of 1004 in exponential form is:
1004 = 22×2511
∴ So by taking common prime factors GCF of 1000 and 1004 is 4
Factors of 1000
List of positive integer factors of 1000 that divides 1000 without a remainder.
1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000
Factors of 1004
List of positive integer factors of 1004 that divides 1004 without a remainder.
1,2,4,251,502,1004
Greatest Common Factor
We found the factors and prime factorization of 1000 and 1004. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1004 is 4.
Also check out the Least Common Multiple of 1000 and 1004
(i) The GCF of 1000 and 1004 is associative
GCF of 1000 and 1004 = GCF of 1004 and 1000
1. What is the GCF of 1000 and 1004?
Answer: GCF of 1000 and 1004 is 4.
2. What are the Factors of 1000?
Answer: Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. There are 16 integers that are factors of 1000. The greatest factor of 1000 is 1000.
3. What are the Factors of 1004?
Answer: Factors of 1004 are 1, 2, 4, 251, 502, 1004. There are 6 integers that are factors of 1004. The greatest factor of 1004 is 1004.
4. How to Find the GCF of 1000 and 1004?
Answer:
Greatest Common Factor of 1000 and 1004 = 4
Step 1: Find the prime factorization of 1000
1000 = 2 x 2 x 2 x 5 x 5 x 5
Step 2: Find the prime factorization of 1004
1004 = 2 x 2 x 251
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 2 = 4
Step 4: Therefore, the greatest common factor of 1000 and 1004 is 4