Greatest Common Factor of 419/13, 132/76, 142/34

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 419/13, 132/76, 142/34

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 419/13,132/76,142/34

Given fractions are 419/13,132/76,142/34

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 419,132,142

Greatest Common Factor of Numerators i.e. GCF of 419,132,142 is 1 .

LCM of Denominators means LCM of 13,76,34 as per the given fractions.

LCM of 13,76,34 is 16796 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 419,132,142

GCF of Fractions 419/13,132/76,142/34 is 1/16796

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

Greatest Common Factor of 419,132,142 By Matching Biggest Common Factor Method

Greatest Common Factor of 419,132,142 By Matching Biggest Common Factor Method

Factors of 419

List of positive integer factors of 419 that divides 419 without a remainder.

1,419

Factors of 132

List of positive integer factors of 132 that divides 132 without a remainder.

1,2,3,4,6,11,12,22,33,44,66,132

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 419,132,142 . The biggest common factor number is the GCF number.
So the greatest common factor 419,132,142 is 1.

Lets's calculate LCM of 13,76,34

2 13, 76, 34
13, 38, 17

∴ So the LCM of the given numbers is 2 x 13 x 38 x 17 = 16796

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16796

Therefore, the GCF of Fractions 419/13,132/76,142/34 is 1/16796

Least Common Multiple of 13,76,34 with GCF Formula

Least Common Multiple of 13,76,34 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 13,76,34 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,76,34) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(13,76,34) x common factors =1 x 2 = 2

LCM(13,76,34) = ( 13 × 76 × 34 ) / 2

LCM(13,76,34) = 33592 / 2

LCM(13,76,34) = 16796


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 419/13, 132/76, 142/34

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 419/13, 132/76, 142/34?

Answer: GCF of Numerators as per given numbers 419/13, 132/76, 142/34 is

GCF of Numerators i.e. for 419,132,142 is 1

LCM of denominators i.e. for 13,76,34 is 16796.

Thus, GCF of Fractions is 1/16796.Finally, GCF of Fractions for 419/13, 132/76, 142/34 is 1/16796.