How to Find GCF of 27/42, 17/246, 273/142?

GCF of 27/42, 17/246, 273/142

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 27/42, 17/246, 273/142 i.e 1/122262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/42, 17/246, 273/142.

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 27/42,17/246,273/142?

Given fractions are 27/42,17/246,273/142

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 27/42,17/246,273/142, numerators are 27,17,273

Denominators are 42,246,142

The GCF of 27,17,273 is 1 .

LCM of 42,246,142 is 122262.

The greatest common factor of 27/42,17/246,273/142 = [GCF of 27,17,273]/[LCM of 42,246,142]= 1/122262

Therefore, the GCF of 27/42,17/246,273/142 is 1/122262.

Greatest Common Factor of 27,17,273

To find the highest common factor of 27,17,273, we have to find the factors of both numbers and list the highest common factor.

The factors of 27 are 1, 3, 9, 27

The factors of 17 are 1, 17

The factors of 273 are 1, 3, 7, 13, 21, 39, 91, 273

The HCF of 27,17,273 is 1.

Lets's calculate GCF of 27,17,273

Greatest Common Factor (GCF) of 27,17,273 By Common Division

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

Greatest Common Factor of 27,17,273 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 17

1,17

Now, list down the factors of 273

1,3,7,13,21,39,91,273

Greatest Common Factor

We found the factors 27,17,273 . The biggest common factor number is the GCF number.
So the greatest common factor 27,17,273 is 1.

Lets's calculate LCM of 42,246,142

Lowest Common Multiple of 42,246,142 using Common Division

2	42, 246, 142
3	21, 123, 71
	7, 41, 71

∴ So the LCM of the given numbers is 2 x 3 x 7 x 41 x 71 = 122262

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122262

Therefore, the GCF of Fractions 27/42,17/246,273/142 is 1/122262

Least Common Multiple of 42,246,142 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 42,246,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,246,142) = 2

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

GCF(42,246,142) x common factors =2 x 6 = 12

LCM(42,246,142) = ( 42 × 246 × 142 ) / 12

LCM(42,246,142) = 1467144 / 12

LCM(42,246,142) = 122262

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FAQs on GCF of Fractions of 27/42, 17/246, 273/142

1. What is the HCF of 27,17,273?

The HCF of 27,17,273 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 27/42, 17/246, 273/142?

Answer: GCF of Numerators as per given numbers 27/42, 17/246, 273/142 is

GCF of Numerators i.e. for 27,17,273 is 1

LCM of denominators i.e. for 42,246,142 is 122262.

Thus, GCF of Fractions is 1/122262.Finally, GCF of Fractions for 27/42, 17/246, 273/142 is 1/122262.