Greatest Common Factor of 414/80, 613/29, 460/30

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 414/80, 613/29, 460/30

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 414/80,613/29,460/30

Given fractions are 414/80,613/29,460/30

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 414,613,460

Greatest Common Factor of Numerators i.e. GCF of 414,613,460 is 1 .

LCM of Denominators means LCM of 80,29,30 as per the given fractions.

LCM of 80,29,30 is 6960 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 414,613,460

GCF of Fractions 414/80,613/29,460/30 is 1/6960

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 414,613,460 By Matching Biggest Common Factor Method

Greatest Common Factor of 414,613,460 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 613

List of positive integer factors of 613 that divides 613 without a remainder.

1,613

Factors of 460

List of positive integer factors of 460 that divides 460 without a remainder.

1,2,4,5,10,20,23,46,92,115,230,460

Greatest Common Factor

We found the factors 414,613,460 . The biggest common factor number is the GCF number.
So the greatest common factor 414,613,460 is 1.

Lets's calculate LCM of 80,29,30

2 80, 29, 30
5 40, 29, 15
8, 29, 3

∴ So the LCM of the given numbers is 2 x 5 x 8 x 29 x 3 = 6960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6960

Therefore, the GCF of Fractions 414/80,613/29,460/30 is 1/6960

Least Common Multiple of 80,29,30 with GCF Formula

Least Common Multiple of 80,29,30 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 80,29,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,29,30) = 1

common factors(in case of two or more numbers have common factors) = 10

GCF(80,29,30) x common factors =1 x 10 = 10

LCM(80,29,30) = ( 80 × 29 × 30 ) / 10

LCM(80,29,30) = 69600 / 10

LCM(80,29,30) = 6960


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 414/80, 613/29, 460/30

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 414/80, 613/29, 460/30?

Answer: GCF of Numerators as per given numbers 414/80, 613/29, 460/30 is

GCF of Numerators i.e. for 414,613,460 is 1

LCM of denominators i.e. for 80,29,30 is 6960.

Thus, GCF of Fractions is 1/6960.Finally, GCF of Fractions for 414/80, 613/29, 460/30 is 1/6960.