Greatest Common Factor of 30/416, 142/678

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 30/416, 142/678

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 30/416,142/678

Given fractions are 30/416,142/678

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 30,142

Greatest Common Factor of Numerators i.e. GCF of 30,142 is 2 .

LCM of Denominators means LCM of 416,678 as per the given fractions.

LCM of 416,678 is 141024 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 30,142

GCF of Fractions 30/416,142/678 is 2/141024

2 30, 142
15, 71

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

Greatest Common Factor of 30,142 By Matching Biggest Common Factor Method

Greatest Common Factor of 30,142 By Matching Biggest Common Factor Method

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Factors of 142

List of positive integer factors of 142 that divides 142 without a remainder.

1,2,71,142

Greatest Common Factor

We found the factors 30,142 . The biggest common factor number is the GCF number.
So the greatest common factor 30,142 is 2.

Lets's calculate LCM of 416,678

2 416, 678
208, 339

∴ So the LCM of the given numbers is 2 x 208 x 339 = 141024

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/141024

Therefore, the GCF of Fractions 30/416,142/678 is 2/141024

Least Common Multiple of 416,678 with GCF Formula

Least Common Multiple of 416,678 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 416,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(416,678) = 2

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

GCF(416,678) x common factors =2 x 1 = 2

LCM(416,678) = ( 416 × 678 ) / 2

LCM(416,678) = 282048 / 2

LCM(416,678) = 141024


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 30/416, 142/678

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 30/416, 142/678?

Answer: GCF of Numerators as per given numbers 30/416, 142/678 is

GCF of Numerators i.e. for 30,142 is 2

LCM of denominators i.e. for 416,678 is 141024.

Thus, GCF of Fractions is 2/141024.Finally, GCF of Fractions for 30/416, 142/678 is 2/141024.