How to Find GCF of 81/27, 86/34, 23/510?

GCF of 81/27, 86/34, 23/510

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 81/27, 86/34, 23/510 i.e 1/4590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 81/27, 86/34, 23/510.

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 81/27,86/34,23/510?

Given fractions are 81/27,86/34,23/510

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 81/27,86/34,23/510, numerators are 81,86,23

Denominators are 27,34,510

The GCF of 81,86,23 is 1 .

LCM of 27,34,510 is 4590.

The greatest common factor of 81/27,86/34,23/510 = [GCF of 81,86,23]/[LCM of 27,34,510]= 1/4590

Therefore, the GCF of 81/27,86/34,23/510 is 1/4590.

Greatest Common Factor of 81,86,23

To find the highest common factor of 81,86,23, we have to find the factors of both numbers and list the highest common factor.

The factors of 81 are 1, 3, 9, 27, 81

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

The factors of 23 are 1, 23

The HCF of 81,86,23 is 1.

Lets's calculate GCF of 81,86,23

Greatest Common Factor (GCF) of 81,86,23 By Common Division

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

Greatest Common Factor of 81,86,23 By Matching Biggest Common Factor Method

Now, list down the factors of 81

1,3,9,27,81

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 23

1,23

Greatest Common Factor

We found the factors 81,86,23 . The biggest common factor number is the GCF number.
So the greatest common factor 81,86,23 is 1.

Lets's calculate LCM of 27,34,510

Lowest Common Multiple of 27,34,510 using Common Division

2	27, 34, 510
3	27, 17, 255
17	9, 17, 85
	9, 1, 5

∴ So the LCM of the given numbers is 2 x 3 x 17 x 9 x 1 x 5 = 4590

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4590

Therefore, the GCF of Fractions 81/27,86/34,23/510 is 1/4590

Least Common Multiple of 27,34,510 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 27,34,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,34,510) = 1

common factors(in case of two or more numbers have common factors) = 102

GCF(27,34,510) x common factors =1 x 102 = 102

LCM(27,34,510) = ( 27 × 34 × 510 ) / 102

LCM(27,34,510) = 468180 / 102

LCM(27,34,510) = 4590

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 81/27, 86/34, 23/510

1. What is the HCF of 81,86,23?

The HCF of 81,86,23 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 81/27, 86/34, 23/510?

Answer: GCF of Numerators as per given numbers 81/27, 86/34, 23/510 is

GCF of Numerators i.e. for 81,86,23 is 1

LCM of denominators i.e. for 27,34,510 is 4590.

Thus, GCF of Fractions is 1/4590.Finally, GCF of Fractions for 81/27, 86/34, 23/510 is 1/4590.