How to Find GCF of 5285/280, 3209/6686?

GCF of 5285/280, 3209/6686

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 5285/280, 3209/6686 i.e 1/936040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5285/280, 3209/6686.

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 5285/280,3209/6686?

Given fractions are 5285/280,3209/6686

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 5285/280,3209/6686, numerators are 5285,3209

Denominators are 280,6686

The GCF of 5285,3209 is 1 .

LCM of 280,6686 is 936040.

The greatest common factor of 5285/280,3209/6686 = [GCF of 5285,3209]/[LCM of 280,6686]= 1/936040

Therefore, the GCF of 5285/280,3209/6686 is 1/936040.

Greatest Common Factor of 5285,3209

To find the highest common factor of 5285,3209, we have to find the factors of both numbers and list the highest common factor.

The factors of 5285 are 1, 5, 7, 35, 151, 755, 1057, 5285

The factors of 3209 are 1, 3209

The HCF of 5285,3209 is 1.

Lets's calculate GCF of 5285,3209

Greatest Common Factor (GCF) of 5285,3209 By Common Division

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

Greatest Common Factor of 5285,3209 By Matching Biggest Common Factor Method

Now, list down the factors of 5285

1,5,7,35,151,755,1057,5285

Now, list down the factors of 3209

1,3209

Greatest Common Factor

We found the factors 5285,3209 . The biggest common factor number is the GCF number.
So the greatest common factor 5285,3209 is 1.

Lets's calculate LCM of 280,6686

Lowest Common Multiple of 280,6686 using Common Division

2	280, 6686
	140, 3343

∴ So the LCM of the given numbers is 2 x 140 x 3343 = 936040

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/936040

Therefore, the GCF of Fractions 5285/280,3209/6686 is 1/936040

Least Common Multiple of 280,6686 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 280,6686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(280,6686) = 2

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

GCF(280,6686) x common factors =2 x 1 = 2

LCM(280,6686) = ( 280 × 6686 ) / 2

LCM(280,6686) = 1872080 / 2

LCM(280,6686) = 936040

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FAQs on GCF of Fractions of 5285/280, 3209/6686

1. What is the HCF of 5285,3209?

The HCF of 5285,3209 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 5285/280, 3209/6686?

Answer: GCF of Numerators as per given numbers 5285/280, 3209/6686 is

GCF of Numerators i.e. for 5285,3209 is 1

LCM of denominators i.e. for 280,6686 is 936040.

Thus, GCF of Fractions is 1/936040.Finally, GCF of Fractions for 5285/280, 3209/6686 is 1/936040.