How to Find GCF of 82/26, 746/21, 540/19?

GCF of 82/26, 746/21, 540/19

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 82/26, 746/21, 540/19 i.e 2/10374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/26, 746/21, 540/19.

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 82/26,746/21,540/19?

Given fractions are 82/26,746/21,540/19

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 82/26,746/21,540/19, numerators are 82,746,540

Denominators are 26,21,19

The GCF of 82,746,540 is 2 .

LCM of 26,21,19 is 10374.

The greatest common factor of 82/26,746/21,540/19 = [GCF of 82,746,540]/[LCM of 26,21,19]= 2/10374

Therefore, the GCF of 82/26,746/21,540/19 is 2/10374.

Greatest Common Factor of 82,746,540

To find the highest common factor of 82,746,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 82 are 1, 2, 41, 82

The factors of 746 are 1, 2, 373, 746

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 82,746,540 is 2.

Lets's calculate GCF of 82,746,540

Greatest Common Factor (GCF) of 82,746,540 By Common Division

2	82, 746, 540
	41, 373, 270

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 82,746,540 By Matching Biggest Common Factor Method

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 746

1,2,373,746

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 82,746,540 . The biggest common factor number is the GCF number.
So the greatest common factor 82,746,540 is 2.

Lets's calculate LCM of 26,21,19

Lowest Common Multiple of 26,21,19 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 10374

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10374

Therefore, the GCF of Fractions 82/26,746/21,540/19 is 2/10374

Least Common Multiple of 26,21,19 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 26,21,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(26,21,19) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(26,21,19) x common factors =1 x 1 = 1

LCM(26,21,19) = ( 26 × 21 × 19 ) / 1

LCM(26,21,19) = 10374 / 1

LCM(26,21,19) = 10374

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FAQs on GCF of Fractions of 82/26, 746/21, 540/19

1. What is the HCF of 82,746,540?

The HCF of 82,746,540 is 2

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 82/26, 746/21, 540/19?

Answer: GCF of Numerators as per given numbers 82/26, 746/21, 540/19 is

GCF of Numerators i.e. for 82,746,540 is 2

LCM of denominators i.e. for 26,21,19 is 10374.

Thus, GCF of Fractions is 2/10374.Finally, GCF of Fractions for 82/26, 746/21, 540/19 is 2/10374.