How to Find GCF of 610/420, 618/404?

GCF of 610/420, 618/404

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 610/420, 618/404 i.e 2/42420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 610/420, 618/404.

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 610/420,618/404?

Given fractions are 610/420,618/404

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 610/420,618/404, numerators are 610,618

Denominators are 420,404

The GCF of 610,618 is 2 .

LCM of 420,404 is 42420.

The greatest common factor of 610/420,618/404 = [GCF of 610,618]/[LCM of 420,404]= 2/42420

Therefore, the GCF of 610/420,618/404 is 2/42420.

Greatest Common Factor of 610,618

To find the highest common factor of 610,618, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 618 are 1, 2, 3, 6, 103, 206, 309, 618

The HCF of 610,618 is 2.

Lets's calculate GCF of 610,618

Greatest Common Factor (GCF) of 610,618 By Common Division

2	610, 618
	305, 309

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

Greatest Common Factor of 610,618 By Matching Biggest Common Factor Method

Now, list down the factors of 610

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

Now, list down the factors of 618

1,2,3,6,103,206,309,618

Greatest Common Factor

We found the factors 610,618 . The biggest common factor number is the GCF number.
So the greatest common factor 610,618 is 2.

Lets's calculate LCM of 420,404

Lowest Common Multiple of 420,404 using Common Division

2	420, 404
2	210, 202
	105, 101

∴ So the LCM of the given numbers is 2 x 2 x 105 x 101 = 42420

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/42420

Therefore, the GCF of Fractions 610/420,618/404 is 2/42420

Least Common Multiple of 420,404 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 420,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(420,404) = 4

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

GCF(420,404) x common factors =4 x 1 = 4

LCM(420,404) = ( 420 × 404 ) / 4

LCM(420,404) = 169680 / 4

LCM(420,404) = 42420

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FAQs on GCF of Fractions of 610/420, 618/404

1. What is the HCF of 610,618?

The HCF of 610,618 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 610/420, 618/404?

Answer: GCF of Numerators as per given numbers 610/420, 618/404 is

GCF of Numerators i.e. for 610,618 is 2

LCM of denominators i.e. for 420,404 is 42420.

Thus, GCF of Fractions is 2/42420.Finally, GCF of Fractions for 610/420, 618/404 is 2/42420.