How to Find GCF of 2186/389, 2806/5714?

GCF of 2186/389, 2806/5714

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 2186/389, 2806/5714 i.e 2/2222746 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2186/389, 2806/5714.

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 2186/389,2806/5714?

Given fractions are 2186/389,2806/5714

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 2186/389,2806/5714, numerators are 2186,2806

Denominators are 389,5714

The GCF of 2186,2806 is 2 .

LCM of 389,5714 is 2222746.

The greatest common factor of 2186/389,2806/5714 = [GCF of 2186,2806]/[LCM of 389,5714]= 2/2222746

Therefore, the GCF of 2186/389,2806/5714 is 2/2222746.

Greatest Common Factor of 2186,2806

To find the highest common factor of 2186,2806, we have to find the factors of both numbers and list the highest common factor.

The factors of 2186 are 1, 2, 1093, 2186

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

The HCF of 2186,2806 is 2.

Lets's calculate GCF of 2186,2806

Greatest Common Factor (GCF) of 2186,2806 By Common Division

2	2186, 2806
	1093, 1403

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

Greatest Common Factor of 2186,2806 By Matching Biggest Common Factor Method

Now, list down the factors of 2186

1,2,1093,2186

Now, list down the factors of 2806

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

Greatest Common Factor

We found the factors 2186,2806 . The biggest common factor number is the GCF number.
So the greatest common factor 2186,2806 is 2.

Lets's calculate LCM of 389,5714

Lowest Common Multiple of 389,5714 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2222746

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2222746

Therefore, the GCF of Fractions 2186/389,2806/5714 is 2/2222746

Least Common Multiple of 389,5714 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 389,5714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(389,5714) = 1

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

GCF(389,5714) x common factors =1 x 1 = 1

LCM(389,5714) = ( 389 × 5714 ) / 1

LCM(389,5714) = 2222746 / 1

LCM(389,5714) = 2222746

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FAQs on GCF of Fractions of 2186/389, 2806/5714

1. What is the HCF of 2186,2806?

The HCF of 2186,2806 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 2186/389, 2806/5714?

Answer: GCF of Numerators as per given numbers 2186/389, 2806/5714 is

GCF of Numerators i.e. for 2186,2806 is 2

LCM of denominators i.e. for 389,5714 is 2222746.

Thus, GCF of Fractions is 2/2222746.Finally, GCF of Fractions for 2186/389, 2806/5714 is 2/2222746.