Greatest Common Factor of 86/43, 38/69, 69/82, 40/312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 86/43, 38/69, 69/82, 40/312

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 86/43,38/69,69/82,40/312

Given fractions are 86/43,38/69,69/82,40/312

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 86,38,69,40

Greatest Common Factor of Numerators i.e. GCF of 86,38,69,40 is 1 .

LCM of Denominators means LCM of 43,69,82,312 as per the given fractions.

LCM of 43,69,82,312 is 12651288 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 86,38,69,40

GCF of Fractions 86/43,38/69,69/82,40/312 is 1/12651288

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

Greatest Common Factor of 86,38,69,40 By Matching Biggest Common Factor Method

Greatest Common Factor of 86,38,69,40 By Matching Biggest Common Factor Method

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1,2,43,86

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 40

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

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

Greatest Common Factor

We found the factors 86,38,69,40 . The biggest common factor number is the GCF number.
So the greatest common factor 86,38,69,40 is 1.

Lets's calculate LCM of 43,69,82,312

2 43, 69, 82, 312
3 43, 69, 41, 156
43, 23, 41, 52

∴ So the LCM of the given numbers is 2 x 3 x 43 x 23 x 41 x 52 = 12651288

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12651288

Therefore, the GCF of Fractions 86/43,38/69,69/82,40/312 is 1/12651288

Least Common Multiple of 43,69,82,312 with GCF Formula

Least Common Multiple of 43,69,82,312 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 43,69,82,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(43,69,82,312) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(43,69,82,312) x common factors =1 x 6 = 6

LCM(43,69,82,312) = ( 43 × 69 × 82 × 312 ) / 6

LCM(43,69,82,312) = 75907728 / 6

LCM(43,69,82,312) = 12651288


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 86/43, 38/69, 69/82, 40/312

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 86/43, 38/69, 69/82, 40/312?

Answer: GCF of Numerators as per given numbers 86/43, 38/69, 69/82, 40/312 is

GCF of Numerators i.e. for 86,38,69,40 is 1

LCM of denominators i.e. for 43,69,82,312 is 12651288.

Thus, GCF of Fractions is 1/12651288.Finally, GCF of Fractions for 86/43, 38/69, 69/82, 40/312 is 1/12651288.