Greatest Common Factor of 1000 and 1005

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, 1005 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1000 and 1005 is 5.

GCF(1000,1005) = 5

GCF of 1000 and 1005

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1000 and 1005

GCF of 1000 and 1005 is 5

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 1005


3 1005
5 335
67 67
1

Prime factors of 1005 are 3,5,67. Prime factorization of 1005 in exponential form is:

1005 = 31×51×671

∴ So by taking common prime factors GCF of 1000 and 1005 is 5

Greatest Common Factor of 1000 and 1005 by matching factors method

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 1005

List of positive integer factors of 1005 that divides 1005 without a remainder.

1,3,5,15,67,201,335,1005

Greatest Common Factor

We found the factors and prime factorization of 1000 and 1005. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1005 is 5.

Also check out the Least Common Multiple of 1000 and 1005

Properties of GCF 1000 and 1005

(i) The GCF of 1000 and 1005 is associative

GCF of 1000 and 1005 = GCF of 1005 and 1000

Related Greatest Common Factor of 1000

Related Greatest Common Factor of 1005

Frequently Asked Questions on GCF of 1000 and 1005

1. What is the GCF of 1000 and 1005?

Answer: GCF of 1000 and 1005 is 5.

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 1005?

Answer: Factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005. There are 8 integers that are factors of 1005. The greatest factor of 1005 is 1005.

4. How to Find the GCF of 1000 and 1005?

Answer:

Greatest Common Factor of 1000 and 1005 = 5

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 1005

1005 = 3 x 5 x 67

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 1000 and 1005 is 5