How to Find GCF of 258/80, 610/9678?

GCF of 258/80, 610/9678

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 258/80, 610/9678 i.e 2/387120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 258/80, 610/9678.

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 258/80,610/9678?

Given fractions are 258/80,610/9678

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 258/80,610/9678, numerators are 258,610

Denominators are 80,9678

The GCF of 258,610 is 2 .

LCM of 80,9678 is 387120.

The greatest common factor of 258/80,610/9678 = [GCF of 258,610]/[LCM of 80,9678]= 2/387120

Therefore, the GCF of 258/80,610/9678 is 2/387120.

Greatest Common Factor of 258,610

To find the highest common factor of 258,610, we have to find the factors of both numbers and list the highest common factor.

The factors of 258 are 1, 2, 3, 6, 43, 86, 129, 258

The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610

The HCF of 258,610 is 2.

Lets's calculate GCF of 258,610

Greatest Common Factor (GCF) of 258,610 By Common Division

2	258, 610
	129, 305

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

Greatest Common Factor of 258,610 By Matching Biggest Common Factor Method

Now, list down the factors of 258

1,2,3,6,43,86,129,258

Now, list down the factors of 610

1,2,5,10,61,122,305,610

Greatest Common Factor

We found the factors 258,610 . The biggest common factor number is the GCF number.
So the greatest common factor 258,610 is 2.

Lets's calculate LCM of 80,9678

Lowest Common Multiple of 80,9678 using Common Division

2	80, 9678
	40, 4839

∴ So the LCM of the given numbers is 2 x 40 x 4839 = 387120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/387120

Therefore, the GCF of Fractions 258/80,610/9678 is 2/387120

Least Common Multiple of 80,9678 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 80,9678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,9678) = 2

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

GCF(80,9678) x common factors =2 x 1 = 2

LCM(80,9678) = ( 80 × 9678 ) / 2

LCM(80,9678) = 774240 / 2

LCM(80,9678) = 387120

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FAQs on GCF of Fractions of 258/80, 610/9678

1. What is the HCF of 258,610?

The HCF of 258,610 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 258/80, 610/9678?

Answer: GCF of Numerators as per given numbers 258/80, 610/9678 is

GCF of Numerators i.e. for 258,610 is 2

LCM of denominators i.e. for 80,9678 is 387120.

Thus, GCF of Fractions is 2/387120.Finally, GCF of Fractions for 258/80, 610/9678 is 2/387120.