How to Find GCF of 386/305, 2806/1609?

GCF of 386/305, 2806/1609

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 386/305, 2806/1609 i.e 2/490745 easily. The following is the detailed procedure to determine the greatest common factor of fractions 386/305, 2806/1609.

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 386/305,2806/1609?

Given fractions are 386/305,2806/1609

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 386/305,2806/1609, numerators are 386,2806

Denominators are 305,1609

The GCF of 386,2806 is 2 .

LCM of 305,1609 is 490745.

The greatest common factor of 386/305,2806/1609 = [GCF of 386,2806]/[LCM of 305,1609]= 2/490745

Therefore, the GCF of 386/305,2806/1609 is 2/490745.

Greatest Common Factor of 386,2806

To find the highest common factor of 386,2806, we have to find the factors of both numbers and list the highest common factor.

The factors of 386 are 1, 2, 193, 386

The factors of 2806 are 1, 2, 23, 46, 61, 122, 1403, 2806

The HCF of 386,2806 is 2.

Lets's calculate GCF of 386,2806

Greatest Common Factor (GCF) of 386,2806 By Common Division

2	386, 2806
	193, 1403

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

Greatest Common Factor of 386,2806 By Matching Biggest Common Factor Method

Now, list down the factors of 386

1,2,193,386

Now, list down the factors of 2806

1,2,23,46,61,122,1403,2806

Greatest Common Factor

We found the factors 386,2806 . The biggest common factor number is the GCF number.
So the greatest common factor 386,2806 is 2.

Lets's calculate LCM of 305,1609

Lowest Common Multiple of 305,1609 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 490745

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/490745

Therefore, the GCF of Fractions 386/305,2806/1609 is 2/490745

Least Common Multiple of 305,1609 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 305,1609 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(305,1609) = 1

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

GCF(305,1609) x common factors =1 x 1 = 1

LCM(305,1609) = ( 305 × 1609 ) / 1

LCM(305,1609) = 490745 / 1

LCM(305,1609) = 490745

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FAQs on GCF of Fractions of 386/305, 2806/1609

1. What is the HCF of 386,2806?

The HCF of 386,2806 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 386/305, 2806/1609?

Answer: GCF of Numerators as per given numbers 386/305, 2806/1609 is

GCF of Numerators i.e. for 386,2806 is 2

LCM of denominators i.e. for 305,1609 is 490745.

Thus, GCF of Fractions is 2/490745.Finally, GCF of Fractions for 386/305, 2806/1609 is 2/490745.