How to Find GCF of 42/334, 54/168, 307/590?

GCF of 42/334, 54/168, 307/590

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 42/334, 54/168, 307/590 i.e 1/8276520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/334, 54/168, 307/590.

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 42/334,54/168,307/590?

Given fractions are 42/334,54/168,307/590

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 42/334,54/168,307/590, numerators are 42,54,307

Denominators are 334,168,590

The GCF of 42,54,307 is 1 .

LCM of 334,168,590 is 8276520.

The greatest common factor of 42/334,54/168,307/590 = [GCF of 42,54,307]/[LCM of 334,168,590]= 1/8276520

Therefore, the GCF of 42/334,54/168,307/590 is 1/8276520.

Greatest Common Factor of 42,54,307

To find the highest common factor of 42,54,307, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 307 are 1, 307

The HCF of 42,54,307 is 1.

Lets's calculate GCF of 42,54,307

Greatest Common Factor (GCF) of 42,54,307 By Common Division

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

Greatest Common Factor of 42,54,307 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 307

1,307

Greatest Common Factor

We found the factors 42,54,307 . The biggest common factor number is the GCF number.
So the greatest common factor 42,54,307 is 1.

Lets's calculate LCM of 334,168,590

Lowest Common Multiple of 334,168,590 using Common Division

2	334, 168, 590
	167, 84, 295

∴ So the LCM of the given numbers is 2 x 167 x 84 x 295 = 8276520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8276520

Therefore, the GCF of Fractions 42/334,54/168,307/590 is 1/8276520

Least Common Multiple of 334,168,590 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 334,168,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(334,168,590) = 2

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

GCF(334,168,590) x common factors =2 x 2 = 4

LCM(334,168,590) = ( 334 × 168 × 590 ) / 4

LCM(334,168,590) = 33106080 / 4

LCM(334,168,590) = 8276520

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 42/334, 54/168, 307/590

1. What is the HCF of 42,54,307?

The HCF of 42,54,307 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 42/334, 54/168, 307/590?

Answer: GCF of Numerators as per given numbers 42/334, 54/168, 307/590 is

GCF of Numerators i.e. for 42,54,307 is 1

LCM of denominators i.e. for 334,168,590 is 8276520.

Thus, GCF of Fractions is 1/8276520.Finally, GCF of Fractions for 42/334, 54/168, 307/590 is 1/8276520.