Greatest Common Factor of 50/31, 45/86, 214/40

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 50/31, 45/86, 214/40

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 50/31,45/86,214/40

Given fractions are 50/31,45/86,214/40

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 50,45,214

Greatest Common Factor of Numerators i.e. GCF of 50,45,214 is 1 .

LCM of Denominators means LCM of 31,86,40 as per the given fractions.

LCM of 31,86,40 is 53320 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 50,45,214

GCF of Fractions 50/31,45/86,214/40 is 1/53320

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

Greatest Common Factor of 50,45,214 By Matching Biggest Common Factor Method

Greatest Common Factor of 50,45,214 By Matching Biggest Common Factor Method

Factors of 50

List of positive integer factors of 50 that divides 50 without a remainder.

1,2,5,10,25,50

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1,2,107,214

Greatest Common Factor

We found the factors 50,45,214 . The biggest common factor number is the GCF number.
So the greatest common factor 50,45,214 is 1.

Lets's calculate LCM of 31,86,40

2 31, 86, 40
31, 43, 20

∴ So the LCM of the given numbers is 2 x 31 x 43 x 20 = 53320

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/53320

Therefore, the GCF of Fractions 50/31,45/86,214/40 is 1/53320

Least Common Multiple of 31,86,40 with GCF Formula

Least Common Multiple of 31,86,40 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 31,86,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,86,40) = 1

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

GCF(31,86,40) x common factors =1 x 2 = 2

LCM(31,86,40) = ( 31 × 86 × 40 ) / 2

LCM(31,86,40) = 106640 / 2

LCM(31,86,40) = 53320


GCF of Fractions Calculation Examples

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GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 50/31, 45/86, 214/40

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 50/31, 45/86, 214/40?

Answer: GCF of Numerators as per given numbers 50/31, 45/86, 214/40 is

GCF of Numerators i.e. for 50,45,214 is 1

LCM of denominators i.e. for 31,86,40 is 53320.

Thus, GCF of Fractions is 1/53320.Finally, GCF of Fractions for 50/31, 45/86, 214/40 is 1/53320.