Greatest Common Factor of 31/14, 83/18, 16/68, 86/36

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 31/14, 83/18, 16/68, 86/36

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 31/14,83/18,16/68,86/36

Given fractions are 31/14,83/18,16/68,86/36

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 31,83,16,86

Greatest Common Factor of Numerators i.e. GCF of 31,83,16,86 is 1 .

LCM of Denominators means LCM of 14,18,68,36 as per the given fractions.

LCM of 14,18,68,36 is 4284 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 31,83,16,86

GCF of Fractions 31/14,83/18,16/68,86/36 is 1/4284

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

Greatest Common Factor of 31,83,16,86 By Matching Biggest Common Factor Method

Greatest Common Factor of 31,83,16,86 By Matching Biggest Common Factor Method

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

Factors of 83

List of positive integer factors of 83 that divides 83 without a remainder.

1,83

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Factors of 86

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

1,2,43,86

Greatest Common Factor

We found the factors 31,83,16,86 . The biggest common factor number is the GCF number.
So the greatest common factor 31,83,16,86 is 1.

Lets's calculate LCM of 14,18,68,36

2 14, 18, 68, 36
2 7, 9, 34, 18
3 7, 9, 17, 9
3 7, 3, 17, 3
7, 1, 17, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 7 x 1 x 17 x 1 = 4284

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4284

Therefore, the GCF of Fractions 31/14,83/18,16/68,86/36 is 1/4284

Least Common Multiple of 14,18,68,36 with GCF Formula

Least Common Multiple of 14,18,68,36 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 14,18,68,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,18,68,36) = 2

common factors(in case of two or more numbers have common factors) = 72

GCF(14,18,68,36) x common factors =2 x 72 = 144

LCM(14,18,68,36) = ( 14 × 18 × 68 × 36 ) / 144

LCM(14,18,68,36) = 616896 / 144

LCM(14,18,68,36) = 4284


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 31/14, 83/18, 16/68, 86/36

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 31/14, 83/18, 16/68, 86/36?

Answer: GCF of Numerators as per given numbers 31/14, 83/18, 16/68, 86/36 is

GCF of Numerators i.e. for 31,83,16,86 is 1

LCM of denominators i.e. for 14,18,68,36 is 4284.

Thus, GCF of Fractions is 1/4284.Finally, GCF of Fractions for 31/14, 83/18, 16/68, 86/36 is 1/4284.