Greatest Common Factor of 1200 and 1204

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, 1204 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1200 and 1204 is 4.

GCF(1200,1204) = 4

GCF of 1200 and 1204

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

GCF of:
and

Greatest Common Factor of 1200 and 1204

GCF of 1200 and 1204 is 4

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 1204


2 1204
2 602
7 301
43 43
1

Prime factors of 1204 are 2,7,43. Prime factorization of 1204 in exponential form is:

1204 = 22×71×431

∴ So by taking common prime factors GCF of 1200 and 1204 is 4

Greatest Common Factor of 1200 and 1204 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 1204

List of positive integer factors of 1204 that divides 1204 without a remainder.

1,2,4,7,14,28,43,86,172,301,602,1204

Greatest Common Factor

We found the factors and prime factorization of 1200 and 1204. The biggest common factor number is the GCF number.
So the greatest common factor 1200 and 1204 is 4.

Also check out the Least Common Multiple of 1200 and 1204

Properties of GCF 1200 and 1204

(i) The GCF of 1200 and 1204 is associative

GCF of 1200 and 1204 = GCF of 1204 and 1200

Related Greatest Common Factor of 1200

Related Greatest Common Factor of 1204

Frequently Asked Questions on GCF of 1200 and 1204

1. What is the GCF of 1200 and 1204?

Answer: GCF of 1200 and 1204 is 4.

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 1204?

Answer: Factors of 1204 are 1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204. There are 12 integers that are factors of 1204. The greatest factor of 1204 is 1204.

4. How to Find the GCF of 1200 and 1204?

Answer:

Greatest Common Factor of 1200 and 1204 = 4

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 1204

1204 = 2 x 2 x 7 x 43

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 1200 and 1204 is 4