How to Find GCF of 21/90, 82/67, 836/17?

GCF of 21/90, 82/67, 836/17

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 21/90, 82/67, 836/17 i.e 1/102510 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/90, 82/67, 836/17.

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 21/90,82/67,836/17?

Given fractions are 21/90,82/67,836/17

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 21/90,82/67,836/17, numerators are 21,82,836

Denominators are 90,67,17

The GCF of 21,82,836 is 1 .

LCM of 90,67,17 is 102510.

The greatest common factor of 21/90,82/67,836/17 = [GCF of 21,82,836]/[LCM of 90,67,17]= 1/102510

Therefore, the GCF of 21/90,82/67,836/17 is 1/102510.

Greatest Common Factor of 21,82,836

To find the highest common factor of 21,82,836, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

The factors of 82 are 1, 2, 41, 82

The factors of 836 are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836

The HCF of 21,82,836 is 1.

Lets's calculate GCF of 21,82,836

Greatest Common Factor (GCF) of 21,82,836 By Common Division

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

Greatest Common Factor of 21,82,836 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 836

1,2,4,11,19,22,38,44,76,209,418,836

Greatest Common Factor

We found the factors 21,82,836 . The biggest common factor number is the GCF number.
So the greatest common factor 21,82,836 is 1.

Lets's calculate LCM of 90,67,17

Lowest Common Multiple of 90,67,17 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 102510

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/102510

Therefore, the GCF of Fractions 21/90,82/67,836/17 is 1/102510

Least Common Multiple of 90,67,17 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 90,67,17 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(90,67,17) = 1

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

GCF(90,67,17) x common factors =1 x 1 = 1

LCM(90,67,17) = ( 90 × 67 × 17 ) / 1

LCM(90,67,17) = 102510 / 1

LCM(90,67,17) = 102510

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 21/90, 82/67, 836/17

1. What is the HCF of 21,82,836?

The HCF of 21,82,836 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 21/90, 82/67, 836/17?

Answer: GCF of Numerators as per given numbers 21/90, 82/67, 836/17 is

GCF of Numerators i.e. for 21,82,836 is 1

LCM of denominators i.e. for 90,67,17 is 102510.

Thus, GCF of Fractions is 1/102510.Finally, GCF of Fractions for 21/90, 82/67, 836/17 is 1/102510.