How to Find GCF of 20/45, 71/36, 254/194?

GCF of 20/45, 71/36, 254/194

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 20/45, 71/36, 254/194 i.e 1/17460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/45, 71/36, 254/194.

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 20/45,71/36,254/194?

Given fractions are 20/45,71/36,254/194

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 20/45,71/36,254/194, numerators are 20,71,254

Denominators are 45,36,194

The GCF of 20,71,254 is 1 .

LCM of 45,36,194 is 17460.

The greatest common factor of 20/45,71/36,254/194 = [GCF of 20,71,254]/[LCM of 45,36,194]= 1/17460

Therefore, the GCF of 20/45,71/36,254/194 is 1/17460.

Greatest Common Factor of 20,71,254

To find the highest common factor of 20,71,254, 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 71 are 1, 71

The factors of 254 are 1, 2, 127, 254

The HCF of 20,71,254 is 1.

Lets's calculate GCF of 20,71,254

Greatest Common Factor (GCF) of 20,71,254 By Common Division

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

Greatest Common Factor of 20,71,254 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 71

1,71

Now, list down the factors of 254

1,2,127,254

Greatest Common Factor

We found the factors 20,71,254 . The biggest common factor number is the GCF number.
So the greatest common factor 20,71,254 is 1.

Lets's calculate LCM of 45,36,194

Lowest Common Multiple of 45,36,194 using Common Division

2	45, 36, 194
3	45, 18, 97
3	15, 6, 97
	5, 2, 97

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 2 x 97 = 17460

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17460

Therefore, the GCF of Fractions 20/45,71/36,254/194 is 1/17460

Least Common Multiple of 45,36,194 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 45,36,194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,36,194) = 1

common factors(in case of two or more numbers have common factors) = 18

GCF(45,36,194) x common factors =1 x 18 = 18

LCM(45,36,194) = ( 45 × 36 × 194 ) / 18

LCM(45,36,194) = 314280 / 18

LCM(45,36,194) = 17460

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FAQs on GCF of Fractions of 20/45, 71/36, 254/194

1. What is the HCF of 20,71,254?

The HCF of 20,71,254 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 20/45, 71/36, 254/194?

Answer: GCF of Numerators as per given numbers 20/45, 71/36, 254/194 is

GCF of Numerators i.e. for 20,71,254 is 1

LCM of denominators i.e. for 45,36,194 is 17460.

Thus, GCF of Fractions is 1/17460.Finally, GCF of Fractions for 20/45, 71/36, 254/194 is 1/17460.