How to Find GCF of 21/398, 82/520, 146/317?

GCF of 21/398, 82/520, 146/317

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 21/398, 82/520, 146/317 i.e 1/32803160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/398, 82/520, 146/317.

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 21/398,82/520,146/317?

Given fractions are 21/398,82/520,146/317

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 21/398,82/520,146/317, numerators are 21,82,146

Denominators are 398,520,317

The GCF of 21,82,146 is 1 .

LCM of 398,520,317 is 32803160.

The greatest common factor of 21/398,82/520,146/317 = [GCF of 21,82,146]/[LCM of 398,520,317]= 1/32803160

Therefore, the GCF of 21/398,82/520,146/317 is 1/32803160.

Greatest Common Factor of 21,82,146

To find the highest common factor of 21,82,146, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

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

The factors of 146 are 1, 2, 73, 146

The HCF of 21,82,146 is 1.

Lets's calculate GCF of 21,82,146

Greatest Common Factor (GCF) of 21,82,146 By Common Division

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

Greatest Common Factor of 21,82,146 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 146

1,2,73,146

Greatest Common Factor

We found the factors 21,82,146 . The biggest common factor number is the GCF number.
So the greatest common factor 21,82,146 is 1.

Lets's calculate LCM of 398,520,317

Lowest Common Multiple of 398,520,317 using Common Division

2	398, 520, 317
	199, 260, 317

∴ So the LCM of the given numbers is 2 x 199 x 260 x 317 = 32803160

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32803160

Therefore, the GCF of Fractions 21/398,82/520,146/317 is 1/32803160

Least Common Multiple of 398,520,317 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 398,520,317 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(398,520,317) = 1

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

GCF(398,520,317) x common factors =1 x 2 = 2

LCM(398,520,317) = ( 398 × 520 × 317 ) / 2

LCM(398,520,317) = 65606320 / 2

LCM(398,520,317) = 32803160

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FAQs on GCF of Fractions of 21/398, 82/520, 146/317

1. What is the HCF of 21,82,146?

The HCF of 21,82,146 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 21/398, 82/520, 146/317?

Answer: GCF of Numerators as per given numbers 21/398, 82/520, 146/317 is

GCF of Numerators i.e. for 21,82,146 is 1

LCM of denominators i.e. for 398,520,317 is 32803160.

Thus, GCF of Fractions is 1/32803160.Finally, GCF of Fractions for 21/398, 82/520, 146/317 is 1/32803160.