Greatest Common Factor of 1000 and 1006

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, 1006 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1000 and 1006 is 2.

GCF(1000,1006) = 2

GCF of 1000 and 1006

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

GCF of:
and

Greatest Common Factor of 1000 and 1006

GCF of 1000 and 1006 is 2

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 1006


2 1006
503 503
1

Prime factors of 1006 are 2,503. Prime factorization of 1006 in exponential form is:

1006 = 21×5031

∴ So by taking common prime factors GCF of 1000 and 1006 is 2

Greatest Common Factor of 1000 and 1006 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 1006

List of positive integer factors of 1006 that divides 1006 without a remainder.

1,2,503,1006

Greatest Common Factor

We found the factors and prime factorization of 1000 and 1006. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1006 is 2.

Also check out the Least Common Multiple of 1000 and 1006

Properties of GCF 1000 and 1006

(i) The GCF of 1000 and 1006 is associative

GCF of 1000 and 1006 = GCF of 1006 and 1000

Related Greatest Common Factor of 1000

Related Greatest Common Factor of 1006

Frequently Asked Questions on GCF of 1000 and 1006

1. What is the GCF of 1000 and 1006?

Answer: GCF of 1000 and 1006 is 2.

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 1006?

Answer: Factors of 1006 are 1, 2, 503, 1006. There are 4 integers that are factors of 1006. The greatest factor of 1006 is 1006.

4. How to Find the GCF of 1000 and 1006?

Answer:

Greatest Common Factor of 1000 and 1006 = 2

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 1006

1006 = 2 x 503

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2

Step 4: Therefore, the greatest common factor of 1000 and 1006 is 2