How to Find GCF of 28/81, 194/82, 705/104?

GCF of 28/81, 194/82, 705/104

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 28/81, 194/82, 705/104 i.e 1/345384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/81, 194/82, 705/104.

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 28/81,194/82,705/104?

Given fractions are 28/81,194/82,705/104

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 28/81,194/82,705/104, numerators are 28,194,705

Denominators are 81,82,104

The GCF of 28,194,705 is 1 .

LCM of 81,82,104 is 345384.

The greatest common factor of 28/81,194/82,705/104 = [GCF of 28,194,705]/[LCM of 81,82,104]= 1/345384

Therefore, the GCF of 28/81,194/82,705/104 is 1/345384.

Greatest Common Factor of 28,194,705

To find the highest common factor of 28,194,705, we have to find the factors of both numbers and list the highest common factor.

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 194 are 1, 2, 97, 194

The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705

The HCF of 28,194,705 is 1.

Lets's calculate GCF of 28,194,705

Greatest Common Factor (GCF) of 28,194,705 By Common Division

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

Greatest Common Factor of 28,194,705 By Matching Biggest Common Factor Method

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 194

1,2,97,194

Now, list down the factors of 705

1,3,5,15,47,141,235,705

Greatest Common Factor

We found the factors 28,194,705 . The biggest common factor number is the GCF number.
So the greatest common factor 28,194,705 is 1.

Lets's calculate LCM of 81,82,104

Lowest Common Multiple of 81,82,104 using Common Division

2	81, 82, 104
	81, 41, 52

∴ So the LCM of the given numbers is 2 x 81 x 41 x 52 = 345384

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/345384

Therefore, the GCF of Fractions 28/81,194/82,705/104 is 1/345384

Least Common Multiple of 81,82,104 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 81,82,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(81,82,104) = 1

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

GCF(81,82,104) x common factors =1 x 2 = 2

LCM(81,82,104) = ( 81 × 82 × 104 ) / 2

LCM(81,82,104) = 690768 / 2

LCM(81,82,104) = 345384

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 28/81, 194/82, 705/104

1. What is the HCF of 28,194,705?

The HCF of 28,194,705 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 28/81, 194/82, 705/104?

Answer: GCF of Numerators as per given numbers 28/81, 194/82, 705/104 is

GCF of Numerators i.e. for 28,194,705 is 1

LCM of denominators i.e. for 81,82,104 is 345384.

Thus, GCF of Fractions is 1/345384.Finally, GCF of Fractions for 28/81, 194/82, 705/104 is 1/345384.