How to Find GCF of 3706/278, 2714/1887?

GCF of 3706/278, 2714/1887

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 3706/278, 2714/1887 i.e 2/524586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3706/278, 2714/1887.

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 3706/278,2714/1887?

Given fractions are 3706/278,2714/1887

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 3706/278,2714/1887, numerators are 3706,2714

Denominators are 278,1887

The GCF of 3706,2714 is 2 .

LCM of 278,1887 is 524586.

The greatest common factor of 3706/278,2714/1887 = [GCF of 3706,2714]/[LCM of 278,1887]= 2/524586

Therefore, the GCF of 3706/278,2714/1887 is 2/524586.

Greatest Common Factor of 3706,2714

To find the highest common factor of 3706,2714, we have to find the factors of both numbers and list the highest common factor.

The factors of 3706 are 1, 2, 17, 34, 109, 218, 1853, 3706

The factors of 2714 are 1, 2, 23, 46, 59, 118, 1357, 2714

The HCF of 3706,2714 is 2.

Lets's calculate GCF of 3706,2714

Greatest Common Factor (GCF) of 3706,2714 By Common Division

2	3706, 2714
	1853, 1357

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

Greatest Common Factor of 3706,2714 By Matching Biggest Common Factor Method

Now, list down the factors of 3706

1,2,17,34,109,218,1853,3706

Now, list down the factors of 2714

1,2,23,46,59,118,1357,2714

Greatest Common Factor

We found the factors 3706,2714 . The biggest common factor number is the GCF number.
So the greatest common factor 3706,2714 is 2.

Lets's calculate LCM of 278,1887

Lowest Common Multiple of 278,1887 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 524586

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/524586

Therefore, the GCF of Fractions 3706/278,2714/1887 is 2/524586

Least Common Multiple of 278,1887 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 278,1887 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(278,1887) = 1

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

GCF(278,1887) x common factors =1 x 1 = 1

LCM(278,1887) = ( 278 × 1887 ) / 1

LCM(278,1887) = 524586 / 1

LCM(278,1887) = 524586

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 3706/278, 2714/1887

1. What is the HCF of 3706,2714?

The HCF of 3706,2714 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 3706/278, 2714/1887?

Answer: GCF of Numerators as per given numbers 3706/278, 2714/1887 is

GCF of Numerators i.e. for 3706,2714 is 2

LCM of denominators i.e. for 278,1887 is 524586.

Thus, GCF of Fractions is 2/524586.Finally, GCF of Fractions for 3706/278, 2714/1887 is 2/524586.