Greatest Common Factor of 1200 and 1208

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 1200, 1208 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1200 and 1208 is 8.

GCF(1200,1208) = 8

GCF of 1200 and 1208

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

GCF of:
and

Greatest Common Factor of 1200 and 1208

GCF of 1200 and 1208 is 8

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 1208


2 1208
2 604
2 302
151 151
1

Prime factors of 1208 are 2,151. Prime factorization of 1208 in exponential form is:

1208 = 23×1511

∴ So by taking common prime factors GCF of 1200 and 1208 is 8

Greatest Common Factor of 1200 and 1208 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 1208

List of positive integer factors of 1208 that divides 1208 without a remainder.

1,2,4,8,151,302,604,1208

Greatest Common Factor

We found the factors and prime factorization of 1200 and 1208. The biggest common factor number is the GCF number.
So the greatest common factor 1200 and 1208 is 8.

Also check out the Least Common Multiple of 1200 and 1208

Properties of GCF 1200 and 1208

(i) The GCF of 1200 and 1208 is associative

GCF of 1200 and 1208 = GCF of 1208 and 1200

Related Greatest Common Factor of 1200

Related Greatest Common Factor of 1208

Frequently Asked Questions on GCF of 1200 and 1208

1. What is the GCF of 1200 and 1208?

Answer: GCF of 1200 and 1208 is 8.

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 1208?

Answer: Factors of 1208 are 1, 2, 4, 8, 151, 302, 604, 1208. There are 8 integers that are factors of 1208. The greatest factor of 1208 is 1208.

4. How to Find the GCF of 1200 and 1208?

Answer:

Greatest Common Factor of 1200 and 1208 = 8

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 1208

1208 = 2 x 2 x 2 x 151

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 1200 and 1208 is 8