How to Find GCF of 5714/442, 7851/9214?

GCF of 5714/442, 7851/9214

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 5714/442, 7851/9214 i.e 1/119782 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5714/442, 7851/9214.

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 5714/442,7851/9214?

Given fractions are 5714/442,7851/9214

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 5714/442,7851/9214, numerators are 5714,7851

Denominators are 442,9214

The GCF of 5714,7851 is 1 .

LCM of 442,9214 is 119782.

The greatest common factor of 5714/442,7851/9214 = [GCF of 5714,7851]/[LCM of 442,9214]= 1/119782

Therefore, the GCF of 5714/442,7851/9214 is 1/119782.

Greatest Common Factor of 5714,7851

To find the highest common factor of 5714,7851, we have to find the factors of both numbers and list the highest common factor.

The factors of 5714 are 1, 2, 2857, 5714

The factors of 7851 are 1, 3, 2617, 7851

The HCF of 5714,7851 is 1.

Lets's calculate GCF of 5714,7851

Greatest Common Factor (GCF) of 5714,7851 By Common Division

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

Greatest Common Factor of 5714,7851 By Matching Biggest Common Factor Method

Now, list down the factors of 5714

1,2,2857,5714

Now, list down the factors of 7851

1,3,2617,7851

Greatest Common Factor

We found the factors 5714,7851 . The biggest common factor number is the GCF number.
So the greatest common factor 5714,7851 is 1.

Lets's calculate LCM of 442,9214

Lowest Common Multiple of 442,9214 using Common Division

2	442, 9214
17	221, 4607
	13, 271

∴ So the LCM of the given numbers is 2 x 17 x 13 x 271 = 119782

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/119782

Therefore, the GCF of Fractions 5714/442,7851/9214 is 1/119782

Least Common Multiple of 442,9214 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 442,9214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(442,9214) = 34

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

GCF(442,9214) x common factors =34 x 1 = 34

LCM(442,9214) = ( 442 × 9214 ) / 34

LCM(442,9214) = 4072588 / 34

LCM(442,9214) = 119782

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FAQs on GCF of Fractions of 5714/442, 7851/9214

1. What is the HCF of 5714,7851?

The HCF of 5714,7851 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 5714/442, 7851/9214?

Answer: GCF of Numerators as per given numbers 5714/442, 7851/9214 is

GCF of Numerators i.e. for 5714,7851 is 1

LCM of denominators i.e. for 442,9214 is 119782.

Thus, GCF of Fractions is 1/119782.Finally, GCF of Fractions for 5714/442, 7851/9214 is 1/119782.