Greatest Common Factor of 2300 and 2304

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 2300, 2304 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2300 and 2304 is 4.

GCF(2300,2304) = 4

GCF of 2300 and 2304

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

GCF of:
and

Greatest Common Factor of 2300 and 2304

GCF of 2300 and 2304 is 4

Prime Factorization of 2300


2 2300
2 1150
5 575
5 115
23 23
1

Prime factors of 2300 are 2,5,23. Prime factorization of 2300 in exponential form is:

2300 = 22×52×231

Prime Factorization of 2304


2 2304
2 1152
2 576
2 288
2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 2304 are 2,3. Prime factorization of 2304 in exponential form is:

2304 = 28×32

∴ So by taking common prime factors GCF of 2300 and 2304 is 4

Greatest Common Factor of 2300 and 2304 by matching factors method

Factors of 2300

List of positive integer factors of 2300 that divides 2300 without a remainder.

1,2,4,5,10,20,23,25,46,50,92,100,115,230,460,575,1150,2300

Factors of 2304

List of positive integer factors of 2304 that divides 2304 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,128,144,192,256,288,384,576,768,1152,2304

Greatest Common Factor

We found the factors and prime factorization of 2300 and 2304. The biggest common factor number is the GCF number.
So the greatest common factor 2300 and 2304 is 4.

Also check out the Least Common Multiple of 2300 and 2304

Properties of GCF 2300 and 2304

(i) The GCF of 2300 and 2304 is associative

GCF of 2300 and 2304 = GCF of 2304 and 2300

Related Greatest Common Factor of 2300

Related Greatest Common Factor of 2304

Frequently Asked Questions on GCF of 2300 and 2304

1. What is the GCF of 2300 and 2304?

Answer: GCF of 2300 and 2304 is 4.

2. What are the Factors of 2300?

Answer: Factors of 2300 are 1, 2, 4, 5, 10, 20, 23, 25, 46, 50, 92, 100, 115, 230, 460, 575, 1150, 2300. There are 18 integers that are factors of 2300. The greatest factor of 2300 is 2300.

3. What are the Factors of 2304?

Answer: Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304. There are 27 integers that are factors of 2304. The greatest factor of 2304 is 2304.

4. How to Find the GCF of 2300 and 2304?

Answer:

Greatest Common Factor of 2300 and 2304 = 4

Step 1: Find the prime factorization of 2300

2300 = 2 x 2 x 5 x 5 x 23

Step 2: Find the prime factorization of 2304

2304 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

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 2300 and 2304 is 4