Greatest Common Factor of 14300 and 14304

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 14300, 14304 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 14300 and 14304 is 4.

GCF(14300,14304) = 4

GCF of 14300 and 14304

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

GCF of:
and

Greatest Common Factor of 14300 and 14304

GCF of 14300 and 14304 is 4

Prime Factorization of 14300


2 14300
2 7150
5 3575
5 715
11 143
13 13
1

Prime factors of 14300 are 2,5,11,13. Prime factorization of 14300 in exponential form is:

14300 = 22×52×111×131

Prime Factorization of 14304


2 14304
2 7152
2 3576
2 1788
2 894
3 447
149 149
1

Prime factors of 14304 are 2,3,149. Prime factorization of 14304 in exponential form is:

14304 = 25×31×1491

∴ So by taking common prime factors GCF of 14300 and 14304 is 4

Greatest Common Factor of 14300 and 14304 by matching factors method

Factors of 14300

List of positive integer factors of 14300 that divides 14300 without a remainder.

1,2,4,5,10,11,13,20,22,25,26,44,50,52,55,65,100,110,130,143,220,260,275,286,325,550,572,650,715,1100,1300,1430,2860,3575,7150,14300

Factors of 14304

List of positive integer factors of 14304 that divides 14304 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,96,149,298,447,596,894,1192,1788,2384,3576,4768,7152,14304

Greatest Common Factor

We found the factors and prime factorization of 14300 and 14304. The biggest common factor number is the GCF number.
So the greatest common factor 14300 and 14304 is 4.

Also check out the Least Common Multiple of 14300 and 14304

Properties of GCF 14300 and 14304

(i) The GCF of 14300 and 14304 is associative

GCF of 14300 and 14304 = GCF of 14304 and 14300

Related Greatest Common Factor of 14300

Related Greatest Common Factor of 14304

Frequently Asked Questions on GCF of 14300 and 14304

1. What is the GCF of 14300 and 14304?

Answer: GCF of 14300 and 14304 is 4.

2. What are the Factors of 14300?

Answer: Factors of 14300 are 1, 2, 4, 5, 10, 11, 13, 20, 22, 25, 26, 44, 50, 52, 55, 65, 100, 110, 130, 143, 220, 260, 275, 286, 325, 550, 572, 650, 715, 1100, 1300, 1430, 2860, 3575, 7150, 14300. There are 36 integers that are factors of 14300. The greatest factor of 14300 is 14300.

3. What are the Factors of 14304?

Answer: Factors of 14304 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 149, 298, 447, 596, 894, 1192, 1788, 2384, 3576, 4768, 7152, 14304. There are 24 integers that are factors of 14304. The greatest factor of 14304 is 14304.

4. How to Find the GCF of 14300 and 14304?

Answer:

Greatest Common Factor of 14300 and 14304 = 4

Step 1: Find the prime factorization of 14300

14300 = 2 x 2 x 5 x 5 x 11 x 13

Step 2: Find the prime factorization of 14304

14304 = 2 x 2 x 2 x 2 x 2 x 3 x 149

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 14300 and 14304 is 4