# Greatest Common Factor of 1200 and 1205

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1200, 1205 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1200 and 1205 is 5.

GCF(1200,1205) = 5

## GCF of 1200 and 1205

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

GCF of:
and

### Greatest Common Factor of 1200 and 1205 by Prime factorization method

Prime Factorization of 1200

 2 1200 2 600 2 300 2 150 3 75 5 25 5 5 1

Prime factors of 1200 are 2,3,5. Prime factorization of 1200 in exponential form is:

1200 = 24×31×52

Prime Factorization of 1205

 5 1205 241 241 1

Prime factors of 1205 are 5,241. Prime factorization of 1205 in exponential form is:

1205 = 51×2411

∴ So by taking common prime factors GCF of 1200 and 1205 is 5

### Greatest Common Factor of 1200 and 1205 by matching factors method

Factors of 1200

List of positive integer factors of 1200 that divides 1200 without a remainder.

1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,40,48,50,60,75,80,100,120,150,200,240,300,400,600,1200

Factors of 1205

List of positive integer factors of 1205 that divides 1205 without a remainder.

1,5,241,1205

Greatest Common Factor

We found the factors and prime factorization of 1200 and 1205. The biggest common factor number is the GCF number.
So the greatest common factor 1200 and 1205 is 5.

Also check out the Least Common Multiple of 1200 and 1205

### Properties of GCF 1200 and 1205

(i) The GCF of 1200 and 1205 is associative

GCF of 1200 and 1205 = GCF of 1205 and 1200

### Frequently Asked Questions on GCF of 1200 and 1205

1. What is the GCF of 1200 and 1205?

Answer: GCF of 1200 and 1205 is 5.

2. What are the Factors of 1200?

Answer: Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200. There are 30 integers that are factors of 1200. The greatest factor of 1200 is 1200.

3. What are the Factors of 1205?

Answer: Factors of 1205 are 1, 5, 241, 1205. There are 4 integers that are factors of 1205. The greatest factor of 1205 is 1205.

4. How to Find the GCF of 1200 and 1205?

Greatest Common Factor of 1200 and 1205 = 5

Step 1: Find the prime factorization of 1200

1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 1205

1205 = 5 x 241

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 1200 and 1205 is 5 