Greatest Common Factor of 1004 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 1004, 1008 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1004 and 1008 is 4.

GCF(1004,1008) = 4

GCF of 1004 and 1008

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

GCF of:
and

Greatest Common Factor of 1004 and 1008

GCF of 1004 and 1008 is 4

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

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 1004 and 1008 is 4

Greatest Common Factor of 1004 and 1008 by matching factors method

Factors of 1004

List of positive integer factors of 1004 that divides 1004 without a remainder.

1,2,4,251,502,1004

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 1004 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 1004 and 1008 is 4.

Also check out the Least Common Multiple of 1004 and 1008

Properties of GCF 1004 and 1008

(i) The GCF of 1004 and 1008 is associative

GCF of 1004 and 1008 = GCF of 1008 and 1004

Related Greatest Common Factor of 1004

Related Greatest Common Factor of 1008

Frequently Asked Questions on GCF of 1004 and 1008

1. What is the GCF of 1004 and 1008?

Answer: GCF of 1004 and 1008 is 4.

2. 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.

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 1004 and 1008?

Answer:

Greatest Common Factor of 1004 and 1008 = 4

Step 1: Find the prime factorization of 1004

1004 = 2 x 2 x 251

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 = 4

Step 4: Therefore, the greatest common factor of 1004 and 1008 is 4