How to Find GCF of 86/12, 19/17, 180/326?

GCF of 86/12, 19/17, 180/326

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 86/12, 19/17, 180/326 i.e 1/33252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/12, 19/17, 180/326.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 86/12,19/17,180/326?

Given fractions are 86/12,19/17,180/326

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 86/12,19/17,180/326, numerators are 86,19,180

Denominators are 12,17,326

The GCF of 86,19,180 is 1 .

LCM of 12,17,326 is 33252.

The greatest common factor of 86/12,19/17,180/326 = [GCF of 86,19,180]/[LCM of 12,17,326]= 1/33252

Therefore, the GCF of 86/12,19/17,180/326 is 1/33252.

Greatest Common Factor of 86,19,180

To find the highest common factor of 86,19,180, we have to find the factors of both numbers and list the highest common factor.

The factors of 86 are 1, 2, 43, 86

The factors of 19 are 1, 19

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The HCF of 86,19,180 is 1.

Lets's calculate GCF of 86,19,180

Greatest Common Factor (GCF) of 86,19,180 By Common Division

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

Greatest Common Factor of 86,19,180 By Matching Biggest Common Factor Method

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 19

1,19

Now, list down the factors of 180

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Greatest Common Factor

We found the factors 86,19,180 . The biggest common factor number is the GCF number.
So the greatest common factor 86,19,180 is 1.

Lets's calculate LCM of 12,17,326

Lowest Common Multiple of 12,17,326 using Common Division

2	12, 17, 326
	6, 17, 163

∴ So the LCM of the given numbers is 2 x 6 x 17 x 163 = 33252

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33252

Therefore, the GCF of Fractions 86/12,19/17,180/326 is 1/33252

Least Common Multiple of 12,17,326 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 12,17,326 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,17,326) = 1

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

GCF(12,17,326) x common factors =1 x 2 = 2

LCM(12,17,326) = ( 12 × 17 × 326 ) / 2

LCM(12,17,326) = 66504 / 2

LCM(12,17,326) = 33252

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 86/12, 19/17, 180/326

1. What is the HCF of 86,19,180?

The HCF of 86,19,180 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 86/12, 19/17, 180/326?

Answer: GCF of Numerators as per given numbers 86/12, 19/17, 180/326 is

GCF of Numerators i.e. for 86,19,180 is 1

LCM of denominators i.e. for 12,17,326 is 33252.

Thus, GCF of Fractions is 1/33252.Finally, GCF of Fractions for 86/12, 19/17, 180/326 is 1/33252.