How to Find GCF of 817/21, 857/61, 521/29?

GCF of 817/21, 857/61, 521/29

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 817/21, 857/61, 521/29 i.e 1/37149 easily. The following is the detailed procedure to determine the greatest common factor of fractions 817/21, 857/61, 521/29.

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 817/21,857/61,521/29?

Given fractions are 817/21,857/61,521/29

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 817/21,857/61,521/29, numerators are 817,857,521

Denominators are 21,61,29

The GCF of 817,857,521 is 1 .

LCM of 21,61,29 is 37149.

The greatest common factor of 817/21,857/61,521/29 = [GCF of 817,857,521]/[LCM of 21,61,29]= 1/37149

Therefore, the GCF of 817/21,857/61,521/29 is 1/37149.

Greatest Common Factor of 817,857,521

To find the highest common factor of 817,857,521, we have to find the factors of both numbers and list the highest common factor.

The factors of 817 are 1, 19, 43, 817

The factors of 857 are 1, 857

The factors of 521 are 1, 521

The HCF of 817,857,521 is 1.

Lets's calculate GCF of 817,857,521

Greatest Common Factor (GCF) of 817,857,521 By Common Division

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

Greatest Common Factor of 817,857,521 By Matching Biggest Common Factor Method

Now, list down the factors of 817

1,19,43,817

Now, list down the factors of 857

1,857

Now, list down the factors of 521

1,521

Greatest Common Factor

We found the factors 817,857,521 . The biggest common factor number is the GCF number.
So the greatest common factor 817,857,521 is 1.

Lets's calculate LCM of 21,61,29

Lowest Common Multiple of 21,61,29 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 37149

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37149

Therefore, the GCF of Fractions 817/21,857/61,521/29 is 1/37149

Least Common Multiple of 21,61,29 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 21,61,29 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,61,29) = 1

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

GCF(21,61,29) x common factors =1 x 1 = 1

LCM(21,61,29) = ( 21 × 61 × 29 ) / 1

LCM(21,61,29) = 37149 / 1

LCM(21,61,29) = 37149

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 817/21, 857/61, 521/29

1. What is the HCF of 817,857,521?

The HCF of 817,857,521 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 817/21, 857/61, 521/29?

Answer: GCF of Numerators as per given numbers 817/21, 857/61, 521/29 is

GCF of Numerators i.e. for 817,857,521 is 1

LCM of denominators i.e. for 21,61,29 is 37149.

Thus, GCF of Fractions is 1/37149.Finally, GCF of Fractions for 817/21, 857/61, 521/29 is 1/37149.