How to Find GCF of 586/661, 3425/409?

GCF of 586/661, 3425/409

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 586/661, 3425/409 i.e 1/270349 easily. The following is the detailed procedure to determine the greatest common factor of fractions 586/661, 3425/409.

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 586/661,3425/409?

Given fractions are 586/661,3425/409

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 586/661,3425/409, numerators are 586,3425

Denominators are 661,409

The GCF of 586,3425 is 1 .

LCM of 661,409 is 270349.

The greatest common factor of 586/661,3425/409 = [GCF of 586,3425]/[LCM of 661,409]= 1/270349

Therefore, the GCF of 586/661,3425/409 is 1/270349.

Greatest Common Factor of 586,3425

To find the highest common factor of 586,3425, we have to find the factors of both numbers and list the highest common factor.

The factors of 586 are 1, 2, 293, 586

The factors of 3425 are 1, 5, 25, 137, 685, 3425

The HCF of 586,3425 is 1.

Lets's calculate GCF of 586,3425

Greatest Common Factor (GCF) of 586,3425 By Common Division

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

Greatest Common Factor of 586,3425 By Matching Biggest Common Factor Method

Now, list down the factors of 586

1,2,293,586

Now, list down the factors of 3425

1,5,25,137,685,3425

Greatest Common Factor

We found the factors 586,3425 . The biggest common factor number is the GCF number.
So the greatest common factor 586,3425 is 1.

Lets's calculate LCM of 661,409

Lowest Common Multiple of 661,409 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 270349

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/270349

Therefore, the GCF of Fractions 586/661,3425/409 is 1/270349

Least Common Multiple of 661,409 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 661,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(661,409) = 1

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

GCF(661,409) x common factors =1 x 1 = 1

LCM(661,409) = ( 661 × 409 ) / 1

LCM(661,409) = 270349 / 1

LCM(661,409) = 270349

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FAQs on GCF of Fractions of 586/661, 3425/409

1. What is the HCF of 586,3425?

The HCF of 586,3425 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 586/661, 3425/409?

Answer: GCF of Numerators as per given numbers 586/661, 3425/409 is

GCF of Numerators i.e. for 586,3425 is 1

LCM of denominators i.e. for 661,409 is 270349.

Thus, GCF of Fractions is 1/270349.Finally, GCF of Fractions for 586/661, 3425/409 is 1/270349.