Greatest Common Factor of 414/21, 860/24, 300/313

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 414/21, 860/24, 300/313

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 414/21,860/24,300/313

Given fractions are 414/21,860/24,300/313

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 414,860,300

Greatest Common Factor of Numerators i.e. GCF of 414,860,300 is 2 .

LCM of Denominators means LCM of 21,24,313 as per the given fractions.

LCM of 21,24,313 is 52584 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 414,860,300

GCF of Fractions 414/21,860/24,300/313 is 2/52584

2 414, 860, 300
207, 430, 150

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 414,860,300 By Matching Biggest Common Factor Method

Greatest Common Factor of 414,860,300 By Matching Biggest Common Factor Method

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Factors of 860

List of positive integer factors of 860 that divides 860 without a remainder.

1,2,4,5,10,20,43,86,172,215,430,860

Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 414,860,300 . The biggest common factor number is the GCF number.
So the greatest common factor 414,860,300 is 2.

Lets's calculate LCM of 21,24,313

3 21, 24, 313
7, 8, 313

∴ So the LCM of the given numbers is 3 x 7 x 8 x 313 = 52584

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/52584

Therefore, the GCF of Fractions 414/21,860/24,300/313 is 2/52584

Least Common Multiple of 21,24,313 with GCF Formula

Least Common Multiple of 21,24,313 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 21,24,313 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,24,313) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(21,24,313) x common factors =1 x 3 = 3

LCM(21,24,313) = ( 21 × 24 × 313 ) / 3

LCM(21,24,313) = 157752 / 3

LCM(21,24,313) = 52584


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 414/21, 860/24, 300/313

1. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

2. What is the GCF of Fractions for 414/21, 860/24, 300/313?

Answer: GCF of Numerators as per given numbers 414/21, 860/24, 300/313 is

GCF of Numerators i.e. for 414,860,300 is 2

LCM of denominators i.e. for 21,24,313 is 52584.

Thus, GCF of Fractions is 2/52584.Finally, GCF of Fractions for 414/21, 860/24, 300/313 is 2/52584.