Greatest Common Factor of 3000 and 3006

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 3000, 3006 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 3000 and 3006 is 6.

GCF(3000,3006) = 6

GCF of 3000 and 3006

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

GCF of:
and

Greatest Common Factor of 3000 and 3006

GCF of 3000 and 3006 is 6

Prime Factorization of 3000


2 3000
2 1500
2 750
3 375
5 125
5 25
5 5
1

Prime factors of 3000 are 2,3,5. Prime factorization of 3000 in exponential form is:

3000 = 23×31×53

Prime Factorization of 3006


2 3006
3 1503
3 501
167 167
1

Prime factors of 3006 are 2,3,167. Prime factorization of 3006 in exponential form is:

3006 = 21×32×1671

∴ So by taking common prime factors GCF of 3000 and 3006 is 6

Greatest Common Factor of 3000 and 3006 by matching factors method

Factors of 3000

List of positive integer factors of 3000 that divides 3000 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,125,150,200,250,300,375,500,600,750,1000,1500,3000

Factors of 3006

List of positive integer factors of 3006 that divides 3006 without a remainder.

1,2,3,6,9,18,167,334,501,1002,1503,3006

Greatest Common Factor

We found the factors and prime factorization of 3000 and 3006. The biggest common factor number is the GCF number.
So the greatest common factor 3000 and 3006 is 6.

Also check out the Least Common Multiple of 3000 and 3006

Properties of GCF 3000 and 3006

(i) The GCF of 3000 and 3006 is associative

GCF of 3000 and 3006 = GCF of 3006 and 3000

Related Greatest Common Factor of 3000

Related Greatest Common Factor of 3006

Frequently Asked Questions on GCF of 3000 and 3006

1. What is the GCF of 3000 and 3006?

Answer: GCF of 3000 and 3006 is 6.

2. What are the Factors of 3000?

Answer: Factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000. There are 32 integers that are factors of 3000. The greatest factor of 3000 is 3000.

3. What are the Factors of 3006?

Answer: Factors of 3006 are 1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006. There are 12 integers that are factors of 3006. The greatest factor of 3006 is 3006.

4. How to Find the GCF of 3000 and 3006?

Answer:

Greatest Common Factor of 3000 and 3006 = 6

Step 1: Find the prime factorization of 3000

3000 = 2 x 2 x 2 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 3006

3006 = 2 x 3 x 3 x 167

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 3000 and 3006 is 6