Greatest Common Factor of 40/414, 310/610

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 40/414, 310/610

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 40/414,310/610

Given fractions are 40/414,310/610

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 40,310

Greatest Common Factor of Numerators i.e. GCF of 40,310 is 10 .

LCM of Denominators means LCM of 414,610 as per the given fractions.

LCM of 414,610 is 126270 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 40,310

GCF of Fractions 40/414,310/610 is 10/126270

2 40, 310
5 20, 155
4, 31

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 40,310 By Matching Biggest Common Factor Method

Greatest Common Factor of 40,310 By Matching Biggest Common Factor Method

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 310

List of positive integer factors of 310 that divides 310 without a remainder.

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 40,310 . The biggest common factor number is the GCF number.
So the greatest common factor 40,310 is 10.

Lets's calculate LCM of 414,610

2 414, 610
207, 305

∴ So the LCM of the given numbers is 2 x 207 x 305 = 126270

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/126270

Therefore, the GCF of Fractions 40/414,310/610 is 10/126270

Least Common Multiple of 414,610 with GCF Formula

Least Common Multiple of 414,610 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 414,610 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(414,610) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(414,610) x common factors =2 x 1 = 2

LCM(414,610) = ( 414 × 610 ) / 2

LCM(414,610) = 252540 / 2

LCM(414,610) = 126270


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 40/414, 310/610

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 40/414, 310/610?

Answer: GCF of Numerators as per given numbers 40/414, 310/610 is

GCF of Numerators i.e. for 40,310 is 10

LCM of denominators i.e. for 414,610 is 126270.

Thus, GCF of Fractions is 10/126270.Finally, GCF of Fractions for 40/414, 310/610 is 10/126270.