Greatest Common Factor of 600 and 605

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 600, 605 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 600 and 605 is 5.

GCF(600,605) = 5

GCF of 600 and 605

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

GCF of:
and

Greatest Common Factor of 600 and 605

GCF of 600 and 605 is 5

Prime Factorization of 600


2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 600 are 2,3,5. Prime factorization of 600 in exponential form is:

600 = 23×31×52

Prime Factorization of 605


5 605
11 121
11 11
1

Prime factors of 605 are 5,11. Prime factorization of 605 in exponential form is:

605 = 51×112

∴ So by taking common prime factors GCF of 600 and 605 is 5

Greatest Common Factor of 600 and 605 by matching factors method

Factors of 600

List of positive integer factors of 600 that divides 600 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600

Factors of 605

List of positive integer factors of 605 that divides 605 without a remainder.

1,5,11,55,121,605

Greatest Common Factor

We found the factors and prime factorization of 600 and 605. The biggest common factor number is the GCF number.
So the greatest common factor 600 and 605 is 5.

Also check out the Least Common Multiple of 600 and 605

Properties of GCF 600 and 605

(i) The GCF of 600 and 605 is associative

GCF of 600 and 605 = GCF of 605 and 600

Related Greatest Common Factor of 600

Related Greatest Common Factor of 605

Frequently Asked Questions on GCF of 600 and 605

1. What is the GCF of 600 and 605?

Answer: GCF of 600 and 605 is 5.

2. What are the Factors of 600?

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

3. What are the Factors of 605?

Answer: Factors of 605 are 1, 5, 11, 55, 121, 605. There are 6 integers that are factors of 605. The greatest factor of 605 is 605.

4. How to Find the GCF of 600 and 605?

Answer:

Greatest Common Factor of 600 and 605 = 5

Step 1: Find the prime factorization of 600

600 = 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 605

605 = 5 x 11 x 11

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

GCF = 5

Step 4: Therefore, the greatest common factor of 600 and 605 is 5