How to Find GCF of 20/17, 40/58, 717/146?

GCF of 20/17, 40/58, 717/146

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 20/17, 40/58, 717/146 i.e 1/71978 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/17, 40/58, 717/146.

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 20/17,40/58,717/146?

Given fractions are 20/17,40/58,717/146

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 20/17,40/58,717/146, numerators are 20,40,717

Denominators are 17,58,146

The GCF of 20,40,717 is 1 .

LCM of 17,58,146 is 71978.

The greatest common factor of 20/17,40/58,717/146 = [GCF of 20,40,717]/[LCM of 17,58,146]= 1/71978

Therefore, the GCF of 20/17,40/58,717/146 is 1/71978.

Greatest Common Factor of 20,40,717

To find the highest common factor of 20,40,717, we have to find the factors of both numbers and list the highest common factor.

The factors of 20 are 1, 2, 4, 5, 10, 20

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The factors of 717 are 1, 3, 239, 717

The HCF of 20,40,717 is 1.

Lets's calculate GCF of 20,40,717

Greatest Common Factor (GCF) of 20,40,717 By Common Division

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

Greatest Common Factor of 20,40,717 By Matching Biggest Common Factor Method

Now, list down the factors of 20

1,2,4,5,10,20

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 717

1,3,239,717

Greatest Common Factor

We found the factors 20,40,717 . The biggest common factor number is the GCF number.
So the greatest common factor 20,40,717 is 1.

Lets's calculate LCM of 17,58,146

Lowest Common Multiple of 17,58,146 using Common Division

2	17, 58, 146
	17, 29, 73

∴ So the LCM of the given numbers is 2 x 17 x 29 x 73 = 71978

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/71978

Therefore, the GCF of Fractions 20/17,40/58,717/146 is 1/71978

Least Common Multiple of 17,58,146 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 17,58,146 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,58,146) = 1

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

GCF(17,58,146) x common factors =1 x 2 = 2

LCM(17,58,146) = ( 17 × 58 × 146 ) / 2

LCM(17,58,146) = 143956 / 2

LCM(17,58,146) = 71978

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 20/17, 40/58, 717/146

1. What is the HCF of 20,40,717?

The HCF of 20,40,717 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 20/17, 40/58, 717/146?

Answer: GCF of Numerators as per given numbers 20/17, 40/58, 717/146 is

GCF of Numerators i.e. for 20,40,717 is 1

LCM of denominators i.e. for 17,58,146 is 71978.

Thus, GCF of Fractions is 1/71978.Finally, GCF of Fractions for 20/17, 40/58, 717/146 is 1/71978.