How to Find GCF of 8541/214, 5357/7164?

GCF of 8541/214, 5357/7164

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 8541/214, 5357/7164 i.e 1/766548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8541/214, 5357/7164.

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 8541/214,5357/7164?

Given fractions are 8541/214,5357/7164

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 8541/214,5357/7164, numerators are 8541,5357

Denominators are 214,7164

The GCF of 8541,5357 is 1 .

LCM of 214,7164 is 766548.

The greatest common factor of 8541/214,5357/7164 = [GCF of 8541,5357]/[LCM of 214,7164]= 1/766548

Therefore, the GCF of 8541/214,5357/7164 is 1/766548.

Greatest Common Factor of 8541,5357

To find the highest common factor of 8541,5357, we have to find the factors of both numbers and list the highest common factor.

The factors of 8541 are 1, 3, 9, 13, 39, 73, 117, 219, 657, 949, 2847, 8541

The factors of 5357 are 1, 11, 487, 5357

The HCF of 8541,5357 is 1.

Lets's calculate GCF of 8541,5357

Greatest Common Factor (GCF) of 8541,5357 By Common Division

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

Greatest Common Factor of 8541,5357 By Matching Biggest Common Factor Method

Now, list down the factors of 8541

1,3,9,13,39,73,117,219,657,949,2847,8541

Now, list down the factors of 5357

1,11,487,5357

Greatest Common Factor

We found the factors 8541,5357 . The biggest common factor number is the GCF number.
So the greatest common factor 8541,5357 is 1.

Lets's calculate LCM of 214,7164

Lowest Common Multiple of 214,7164 using Common Division

2	214, 7164
	107, 3582

∴ So the LCM of the given numbers is 2 x 107 x 3582 = 766548

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/766548

Therefore, the GCF of Fractions 8541/214,5357/7164 is 1/766548

Least Common Multiple of 214,7164 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 214,7164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,7164) = 2

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

GCF(214,7164) x common factors =2 x 1 = 2

LCM(214,7164) = ( 214 × 7164 ) / 2

LCM(214,7164) = 1533096 / 2

LCM(214,7164) = 766548

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FAQs on GCF of Fractions of 8541/214, 5357/7164

1. What is the HCF of 8541,5357?

The HCF of 8541,5357 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 8541/214, 5357/7164?

Answer: GCF of Numerators as per given numbers 8541/214, 5357/7164 is

GCF of Numerators i.e. for 8541,5357 is 1

LCM of denominators i.e. for 214,7164 is 766548.

Thus, GCF of Fractions is 1/766548.Finally, GCF of Fractions for 8541/214, 5357/7164 is 1/766548.