Greatest Common Factor of 1000 and 1008

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, 1008 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1000 and 1008 is 8.

GCF(1000,1008) = 8

GCF of 1000 and 1008

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

GCF of:
and

Greatest Common Factor of 1000 and 1008

GCF of 1000 and 1008 is 8

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 1008


2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 1008 are 2,3,7. Prime factorization of 1008 in exponential form is:

1008 = 24×32×71

∴ So by taking common prime factors GCF of 1000 and 1008 is 8

Greatest Common Factor of 1000 and 1008 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 1008

List of positive integer factors of 1008 that divides 1008 without a remainder.

1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,36,42,48,56,63,72,84,112,126,144,168,252,336,504,1008

Greatest Common Factor

We found the factors and prime factorization of 1000 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1008 is 8.

Also check out the Least Common Multiple of 1000 and 1008

Properties of GCF 1000 and 1008

(i) The GCF of 1000 and 1008 is associative

GCF of 1000 and 1008 = GCF of 1008 and 1000

Related Greatest Common Factor of 1000

Related Greatest Common Factor of 1008

Frequently Asked Questions on GCF of 1000 and 1008

1. What is the GCF of 1000 and 1008?

Answer: GCF of 1000 and 1008 is 8.

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 1008?

Answer: Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. There are 30 integers that are factors of 1008. The greatest factor of 1008 is 1008.

4. How to Find the GCF of 1000 and 1008?

Answer:

Greatest Common Factor of 1000 and 1008 = 8

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 1008

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 1000 and 1008 is 8