How to Find GCF of 20/720, 21/916, 719/744?

GCF of 20/720, 21/916, 719/744

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 20/720, 21/916, 719/744 i.e 1/5111280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/720, 21/916, 719/744.

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 20/720,21/916,719/744?

Given fractions are 20/720,21/916,719/744

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 20/720,21/916,719/744, numerators are 20,21,719

Denominators are 720,916,744

The GCF of 20,21,719 is 1 .

LCM of 720,916,744 is 5111280.

The greatest common factor of 20/720,21/916,719/744 = [GCF of 20,21,719]/[LCM of 720,916,744]= 1/5111280

Therefore, the GCF of 20/720,21/916,719/744 is 1/5111280.

Greatest Common Factor of 20,21,719

To find the highest common factor of 20,21,719, 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 21 are 1, 3, 7, 21

The factors of 719 are 1, 719

The HCF of 20,21,719 is 1.

Lets's calculate GCF of 20,21,719

Greatest Common Factor (GCF) of 20,21,719 By Common Division

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

Greatest Common Factor of 20,21,719 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 21

1,3,7,21

Now, list down the factors of 719

1,719

Greatest Common Factor

We found the factors 20,21,719 . The biggest common factor number is the GCF number.
So the greatest common factor 20,21,719 is 1.

Lets's calculate LCM of 720,916,744

Lowest Common Multiple of 720,916,744 using Common Division

2	720, 916, 744
2	360, 458, 372
2	180, 229, 186
3	90, 229, 93
	30, 229, 31

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 30 x 229 x 31 = 5111280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5111280

Therefore, the GCF of Fractions 20/720,21/916,719/744 is 1/5111280

Least Common Multiple of 720,916,744 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 720,916,744 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(720,916,744) = 4

common factors(in case of two or more numbers have common factors) = 24

GCF(720,916,744) x common factors =4 x 24 = 96

LCM(720,916,744) = ( 720 × 916 × 744 ) / 96

LCM(720,916,744) = 490682880 / 96

LCM(720,916,744) = 5111280

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 20/720, 21/916, 719/744

1. What is the HCF of 20,21,719?

The HCF of 20,21,719 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 20/720, 21/916, 719/744?

Answer: GCF of Numerators as per given numbers 20/720, 21/916, 719/744 is

GCF of Numerators i.e. for 20,21,719 is 1

LCM of denominators i.e. for 720,916,744 is 5111280.

Thus, GCF of Fractions is 1/5111280.Finally, GCF of Fractions for 20/720, 21/916, 719/744 is 1/5111280.