How to Find GCF of 206/410, 323/681, 584/814?

GCF of 206/410, 323/681, 584/814

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 206/410, 323/681, 584/814 i.e 1/113638470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/410, 323/681, 584/814.

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 206/410,323/681,584/814?

Given fractions are 206/410,323/681,584/814

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 206/410,323/681,584/814, numerators are 206,323,584

Denominators are 410,681,814

The GCF of 206,323,584 is 1 .

LCM of 410,681,814 is 113638470.

The greatest common factor of 206/410,323/681,584/814 = [GCF of 206,323,584]/[LCM of 410,681,814]= 1/113638470

Therefore, the GCF of 206/410,323/681,584/814 is 1/113638470.

Greatest Common Factor of 206,323,584

To find the highest common factor of 206,323,584, we have to find the factors of both numbers and list the highest common factor.

The factors of 206 are 1, 2, 103, 206

The factors of 323 are 1, 17, 19, 323

The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584

The HCF of 206,323,584 is 1.

Lets's calculate GCF of 206,323,584

Greatest Common Factor (GCF) of 206,323,584 By Common Division

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

Greatest Common Factor of 206,323,584 By Matching Biggest Common Factor Method

Now, list down the factors of 206

1,2,103,206

Now, list down the factors of 323

1,17,19,323

Now, list down the factors of 584

1,2,4,8,73,146,292,584

Greatest Common Factor

We found the factors 206,323,584 . The biggest common factor number is the GCF number.
So the greatest common factor 206,323,584 is 1.

Lets's calculate LCM of 410,681,814

Lowest Common Multiple of 410,681,814 using Common Division

2	410, 681, 814
	205, 681, 407

∴ So the LCM of the given numbers is 2 x 205 x 681 x 407 = 113638470

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/113638470

Therefore, the GCF of Fractions 206/410,323/681,584/814 is 1/113638470

Least Common Multiple of 410,681,814 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 410,681,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(410,681,814) = 1

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

GCF(410,681,814) x common factors =1 x 2 = 2

LCM(410,681,814) = ( 410 × 681 × 814 ) / 2

LCM(410,681,814) = 227276940 / 2

LCM(410,681,814) = 113638470

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 206/410, 323/681, 584/814

1. What is the HCF of 206,323,584?

The HCF of 206,323,584 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 206/410, 323/681, 584/814?

Answer: GCF of Numerators as per given numbers 206/410, 323/681, 584/814 is

GCF of Numerators i.e. for 206,323,584 is 1

LCM of denominators i.e. for 410,681,814 is 113638470.

Thus, GCF of Fractions is 1/113638470.Finally, GCF of Fractions for 206/410, 323/681, 584/814 is 1/113638470.