How to Find GCF of 17/91, 567/55, 138/12?

GCF of 17/91, 567/55, 138/12

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 17/91, 567/55, 138/12 i.e 1/60060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/91, 567/55, 138/12.

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 17/91,567/55,138/12?

Given fractions are 17/91,567/55,138/12

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 17/91,567/55,138/12, numerators are 17,567,138

Denominators are 91,55,12

The GCF of 17,567,138 is 1 .

LCM of 91,55,12 is 60060.

The greatest common factor of 17/91,567/55,138/12 = [GCF of 17,567,138]/[LCM of 91,55,12]= 1/60060

Therefore, the GCF of 17/91,567/55,138/12 is 1/60060.

Greatest Common Factor of 17,567,138

To find the highest common factor of 17,567,138, 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 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567

The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138

The HCF of 17,567,138 is 1.

Lets's calculate GCF of 17,567,138

Greatest Common Factor (GCF) of 17,567,138 By Common Division

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

Greatest Common Factor of 17,567,138 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 567

1,3,7,9,21,27,63,81,189,567

Now, list down the factors of 138

1,2,3,6,23,46,69,138

Greatest Common Factor

We found the factors 17,567,138 . The biggest common factor number is the GCF number.
So the greatest common factor 17,567,138 is 1.

Lets's calculate LCM of 91,55,12

Lowest Common Multiple of 91,55,12 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 60060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/60060

Therefore, the GCF of Fractions 17/91,567/55,138/12 is 1/60060

Least Common Multiple of 91,55,12 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 91,55,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(91,55,12) = 1

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

GCF(91,55,12) x common factors =1 x 1 = 1

LCM(91,55,12) = ( 91 × 55 × 12 ) / 1

LCM(91,55,12) = 60060 / 1

LCM(91,55,12) = 60060

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/91, 567/55, 138/12

1. What is the HCF of 17,567,138?

The HCF of 17,567,138 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 17/91, 567/55, 138/12?

Answer: GCF of Numerators as per given numbers 17/91, 567/55, 138/12 is

GCF of Numerators i.e. for 17,567,138 is 1

LCM of denominators i.e. for 91,55,12 is 60060.

Thus, GCF of Fractions is 1/60060.Finally, GCF of Fractions for 17/91, 567/55, 138/12 is 1/60060.