Greatest Common Factor of 10004 and 10010

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 10004, 10010 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 10004 and 10010 is 2.

GCF(10004,10010) = 2

GCF of 10004 and 10010

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

GCF of:
and

Greatest Common Factor of 10004 and 10010

GCF of 10004 and 10010 is 2

Prime Factorization of 10004


2 10004
2 5002
41 2501
61 61
1

Prime factors of 10004 are 2,41,61. Prime factorization of 10004 in exponential form is:

10004 = 22×411×611

Prime Factorization of 10010


2 10010
5 5005
7 1001
11 143
13 13
1

Prime factors of 10010 are 2,5,7,11,13. Prime factorization of 10010 in exponential form is:

10010 = 21×51×71×111×131

∴ So by taking common prime factors GCF of 10004 and 10010 is 2

Greatest Common Factor of 10004 and 10010 by matching factors method

Factors of 10004

List of positive integer factors of 10004 that divides 10004 without a remainder.

1,2,4,41,61,82,122,164,244,2501,5002,10004

Factors of 10010

List of positive integer factors of 10010 that divides 10010 without a remainder.

1,2,5,7,10,11,13,14,22,26,35,55,65,70,77,91,110,130,143,154,182,286,385,455,715,770,910,1001,1430,2002,5005,10010

Greatest Common Factor

We found the factors and prime factorization of 10004 and 10010. The biggest common factor number is the GCF number.
So the greatest common factor 10004 and 10010 is 2.

Also check out the Least Common Multiple of 10004 and 10010

Properties of GCF 10004 and 10010

(i) The GCF of 10004 and 10010 is associative

GCF of 10004 and 10010 = GCF of 10010 and 10004

Related Greatest Common Factor of 10004

Related Greatest Common Factor of 10010

Frequently Asked Questions on GCF of 10004 and 10010

1. What is the GCF of 10004 and 10010?

Answer: GCF of 10004 and 10010 is 2.

2. What are the Factors of 10004?

Answer: Factors of 10004 are 1, 2, 4, 41, 61, 82, 122, 164, 244, 2501, 5002, 10004. There are 12 integers that are factors of 10004. The greatest factor of 10004 is 10004.

3. What are the Factors of 10010?

Answer: Factors of 10010 are 1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010. There are 32 integers that are factors of 10010. The greatest factor of 10010 is 10010.

4. How to Find the GCF of 10004 and 10010?

Answer:

Greatest Common Factor of 10004 and 10010 = 2

Step 1: Find the prime factorization of 10004

10004 = 2 x 2 x 41 x 61

Step 2: Find the prime factorization of 10010

10010 = 2 x 5 x 7 x 11 x 13

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 10004 and 10010 is 2