How to Find GCF of 61/78, 290/66, 589/298?

GCF of 61/78, 290/66, 589/298

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 61/78, 290/66, 589/298 i.e 1/127842 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/78, 290/66, 589/298.

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 61/78,290/66,589/298?

Given fractions are 61/78,290/66,589/298

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 61/78,290/66,589/298, numerators are 61,290,589

Denominators are 78,66,298

The GCF of 61,290,589 is 1 .

LCM of 78,66,298 is 127842.

The greatest common factor of 61/78,290/66,589/298 = [GCF of 61,290,589]/[LCM of 78,66,298]= 1/127842

Therefore, the GCF of 61/78,290/66,589/298 is 1/127842.

Greatest Common Factor of 61,290,589

To find the highest common factor of 61,290,589, we have to find the factors of both numbers and list the highest common factor.

The factors of 61 are 1, 61

The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290

The factors of 589 are 1, 19, 31, 589

The HCF of 61,290,589 is 1.

Lets's calculate GCF of 61,290,589

Greatest Common Factor (GCF) of 61,290,589 By Common Division

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

Greatest Common Factor of 61,290,589 By Matching Biggest Common Factor Method

Now, list down the factors of 61

1,61

Now, list down the factors of 290

1,2,5,10,29,58,145,290

Now, list down the factors of 589

1,19,31,589

Greatest Common Factor

We found the factors 61,290,589 . The biggest common factor number is the GCF number.
So the greatest common factor 61,290,589 is 1.

Lets's calculate LCM of 78,66,298

Lowest Common Multiple of 78,66,298 using Common Division

2	78, 66, 298
3	39, 33, 149
	13, 11, 149

∴ So the LCM of the given numbers is 2 x 3 x 13 x 11 x 149 = 127842

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/127842

Therefore, the GCF of Fractions 61/78,290/66,589/298 is 1/127842

Least Common Multiple of 78,66,298 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 78,66,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,66,298) = 2

common factors(in case of two or more numbers have common factors) = 6

GCF(78,66,298) x common factors =2 x 6 = 12

LCM(78,66,298) = ( 78 × 66 × 298 ) / 12

LCM(78,66,298) = 1534104 / 12

LCM(78,66,298) = 127842

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FAQs on GCF of Fractions of 61/78, 290/66, 589/298

1. What is the HCF of 61,290,589?

The HCF of 61,290,589 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 61/78, 290/66, 589/298?

Answer: GCF of Numerators as per given numbers 61/78, 290/66, 589/298 is

GCF of Numerators i.e. for 61,290,589 is 1

LCM of denominators i.e. for 78,66,298 is 127842.

Thus, GCF of Fractions is 1/127842.Finally, GCF of Fractions for 61/78, 290/66, 589/298 is 1/127842.