How to Find GCF of 46/76, 82/10, 309/594?

GCF of 46/76, 82/10, 309/594

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 46/76, 82/10, 309/594 i.e 1/112860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/76, 82/10, 309/594.

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 46/76,82/10,309/594?

Given fractions are 46/76,82/10,309/594

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 46/76,82/10,309/594, numerators are 46,82,309

Denominators are 76,10,594

The GCF of 46,82,309 is 1 .

LCM of 76,10,594 is 112860.

The greatest common factor of 46/76,82/10,309/594 = [GCF of 46,82,309]/[LCM of 76,10,594]= 1/112860

Therefore, the GCF of 46/76,82/10,309/594 is 1/112860.

Greatest Common Factor of 46,82,309

To find the highest common factor of 46,82,309, we have to find the factors of both numbers and list the highest common factor.

The factors of 46 are 1, 2, 23, 46

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

The factors of 309 are 1, 3, 103, 309

The HCF of 46,82,309 is 1.

Lets's calculate GCF of 46,82,309

Greatest Common Factor (GCF) of 46,82,309 By Common Division

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

Greatest Common Factor of 46,82,309 By Matching Biggest Common Factor Method

Now, list down the factors of 46

1,2,23,46

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 309

1,3,103,309

Greatest Common Factor

We found the factors 46,82,309 . The biggest common factor number is the GCF number.
So the greatest common factor 46,82,309 is 1.

Lets's calculate LCM of 76,10,594

Lowest Common Multiple of 76,10,594 using Common Division

2	76, 10, 594
	38, 5, 297

∴ So the LCM of the given numbers is 2 x 38 x 5 x 297 = 112860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/112860

Therefore, the GCF of Fractions 46/76,82/10,309/594 is 1/112860

Least Common Multiple of 76,10,594 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 76,10,594 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,10,594) = 2

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

GCF(76,10,594) x common factors =2 x 2 = 4

LCM(76,10,594) = ( 76 × 10 × 594 ) / 4

LCM(76,10,594) = 451440 / 4

LCM(76,10,594) = 112860

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FAQs on GCF of Fractions of 46/76, 82/10, 309/594

1. What is the HCF of 46,82,309?

The HCF of 46,82,309 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 46/76, 82/10, 309/594?

Answer: GCF of Numerators as per given numbers 46/76, 82/10, 309/594 is

GCF of Numerators i.e. for 46,82,309 is 1

LCM of denominators i.e. for 76,10,594 is 112860.

Thus, GCF of Fractions is 1/112860.Finally, GCF of Fractions for 46/76, 82/10, 309/594 is 1/112860.