Greatest Common Factor of 12300 and 12305

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 12300, 12305 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 12300 and 12305 is 5.

GCF(12300,12305) = 5

GCF of 12300 and 12305

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

GCF of:
and

Greatest Common Factor of 12300 and 12305

GCF of 12300 and 12305 is 5

Prime Factorization of 12300


2 12300
2 6150
3 3075
5 1025
5 205
41 41
1

Prime factors of 12300 are 2,3,5,41. Prime factorization of 12300 in exponential form is:

12300 = 22×31×52×411

Prime Factorization of 12305


5 12305
23 2461
107 107
1

Prime factors of 12305 are 5,23,107. Prime factorization of 12305 in exponential form is:

12305 = 51×231×1071

∴ So by taking common prime factors GCF of 12300 and 12305 is 5

Greatest Common Factor of 12300 and 12305 by matching factors method

Factors of 12300

List of positive integer factors of 12300 that divides 12300 without a remainder.

1,2,3,4,5,6,10,12,15,20,25,30,41,50,60,75,82,100,123,150,164,205,246,300,410,492,615,820,1025,1230,2050,2460,3075,4100,6150,12300

Factors of 12305

List of positive integer factors of 12305 that divides 12305 without a remainder.

1,5,23,107,115,535,2461,12305

Greatest Common Factor

We found the factors and prime factorization of 12300 and 12305. The biggest common factor number is the GCF number.
So the greatest common factor 12300 and 12305 is 5.

Also check out the Least Common Multiple of 12300 and 12305

Properties of GCF 12300 and 12305

(i) The GCF of 12300 and 12305 is associative

GCF of 12300 and 12305 = GCF of 12305 and 12300

Related Greatest Common Factor of 12300

Related Greatest Common Factor of 12305

Frequently Asked Questions on GCF of 12300 and 12305

1. What is the GCF of 12300 and 12305?

Answer: GCF of 12300 and 12305 is 5.

2. What are the Factors of 12300?

Answer: Factors of 12300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 41, 50, 60, 75, 82, 100, 123, 150, 164, 205, 246, 300, 410, 492, 615, 820, 1025, 1230, 2050, 2460, 3075, 4100, 6150, 12300. There are 36 integers that are factors of 12300. The greatest factor of 12300 is 12300.

3. What are the Factors of 12305?

Answer: Factors of 12305 are 1, 5, 23, 107, 115, 535, 2461, 12305. There are 8 integers that are factors of 12305. The greatest factor of 12305 is 12305.

4. How to Find the GCF of 12300 and 12305?

Answer:

Greatest Common Factor of 12300 and 12305 = 5

Step 1: Find the prime factorization of 12300

12300 = 2 x 2 x 3 x 5 x 5 x 41

Step 2: Find the prime factorization of 12305

12305 = 5 x 23 x 107

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 12300 and 12305 is 5