How to Find GCF of 17/66, 86/18, 210/498?

GCF of 17/66, 86/18, 210/498

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 17/66, 86/18, 210/498 i.e 1/16434 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/66, 86/18, 210/498.

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 17/66,86/18,210/498?

Given fractions are 17/66,86/18,210/498

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 17/66,86/18,210/498, numerators are 17,86,210

Denominators are 66,18,498

The GCF of 17,86,210 is 1 .

LCM of 66,18,498 is 16434.

The greatest common factor of 17/66,86/18,210/498 = [GCF of 17,86,210]/[LCM of 66,18,498]= 1/16434

Therefore, the GCF of 17/66,86/18,210/498 is 1/16434.

Greatest Common Factor of 17,86,210

To find the highest common factor of 17,86,210, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 86 are 1, 2, 43, 86

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 17,86,210 is 1.

Lets's calculate GCF of 17,86,210

Greatest Common Factor (GCF) of 17,86,210 By Common Division

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

Greatest Common Factor of 17,86,210 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 210

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 17,86,210 . The biggest common factor number is the GCF number.
So the greatest common factor 17,86,210 is 1.

Lets's calculate LCM of 66,18,498

Lowest Common Multiple of 66,18,498 using Common Division

2	66, 18, 498
3	33, 9, 249
	11, 3, 83

∴ So the LCM of the given numbers is 2 x 3 x 11 x 3 x 83 = 16434

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16434

Therefore, the GCF of Fractions 17/66,86/18,210/498 is 1/16434

Least Common Multiple of 66,18,498 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 66,18,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,18,498) = 6

common factors(in case of two or more numbers have common factors) = 6

GCF(66,18,498) x common factors =6 x 6 = 36

LCM(66,18,498) = ( 66 × 18 × 498 ) / 36

LCM(66,18,498) = 591624 / 36

LCM(66,18,498) = 16434

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/66, 86/18, 210/498

1. What is the HCF of 17,86,210?

The HCF of 17,86,210 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 17/66, 86/18, 210/498?

Answer: GCF of Numerators as per given numbers 17/66, 86/18, 210/498 is

GCF of Numerators i.e. for 17,86,210 is 1

LCM of denominators i.e. for 66,18,498 is 16434.

Thus, GCF of Fractions is 1/16434.Finally, GCF of Fractions for 17/66, 86/18, 210/498 is 1/16434.