How to Find GCF of 27/49, 838/16, 189/194?

GCF of 27/49, 838/16, 189/194

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 27/49, 838/16, 189/194 i.e 1/76048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/49, 838/16, 189/194.

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 27/49,838/16,189/194?

Given fractions are 27/49,838/16,189/194

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 27/49,838/16,189/194, numerators are 27,838,189

Denominators are 49,16,194

The GCF of 27,838,189 is 1 .

LCM of 49,16,194 is 76048.

The greatest common factor of 27/49,838/16,189/194 = [GCF of 27,838,189]/[LCM of 49,16,194]= 1/76048

Therefore, the GCF of 27/49,838/16,189/194 is 1/76048.

Greatest Common Factor of 27,838,189

To find the highest common factor of 27,838,189, 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 838 are 1, 2, 419, 838

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189

The HCF of 27,838,189 is 1.

Lets's calculate GCF of 27,838,189

Greatest Common Factor (GCF) of 27,838,189 By Common Division

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

Greatest Common Factor of 27,838,189 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 838

1,2,419,838

Now, list down the factors of 189

1,3,7,9,21,27,63,189

Greatest Common Factor

We found the factors 27,838,189 . The biggest common factor number is the GCF number.
So the greatest common factor 27,838,189 is 1.

Lets's calculate LCM of 49,16,194

Lowest Common Multiple of 49,16,194 using Common Division

2	49, 16, 194
	49, 8, 97

∴ So the LCM of the given numbers is 2 x 49 x 8 x 97 = 76048

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/76048

Therefore, the GCF of Fractions 27/49,838/16,189/194 is 1/76048

Least Common Multiple of 49,16,194 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 49,16,194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(49,16,194) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(49,16,194) x common factors =1 x 2 = 2

LCM(49,16,194) = ( 49 × 16 × 194 ) / 2

LCM(49,16,194) = 152096 / 2

LCM(49,16,194) = 76048

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FAQs on GCF of Fractions of 27/49, 838/16, 189/194

1. What is the HCF of 27,838,189?

The HCF of 27,838,189 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 27/49, 838/16, 189/194?

Answer: GCF of Numerators as per given numbers 27/49, 838/16, 189/194 is

GCF of Numerators i.e. for 27,838,189 is 1

LCM of denominators i.e. for 49,16,194 is 76048.

Thus, GCF of Fractions is 1/76048.Finally, GCF of Fractions for 27/49, 838/16, 189/194 is 1/76048.