How to Find GCF of 72/35, 30/40, 409/13?

GCF of 72/35, 30/40, 409/13

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 72/35, 30/40, 409/13 i.e 1/3640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/35, 30/40, 409/13.

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 72/35,30/40,409/13?

Given fractions are 72/35,30/40,409/13

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 72/35,30/40,409/13, numerators are 72,30,409

Denominators are 35,40,13

The GCF of 72,30,409 is 1 .

LCM of 35,40,13 is 3640.

The greatest common factor of 72/35,30/40,409/13 = [GCF of 72,30,409]/[LCM of 35,40,13]= 1/3640

Therefore, the GCF of 72/35,30/40,409/13 is 1/3640.

Greatest Common Factor of 72,30,409

To find the highest common factor of 72,30,409, we have to find the factors of both numbers and list the highest common factor.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 409 are 1, 409

The HCF of 72,30,409 is 1.

Lets's calculate GCF of 72,30,409

Greatest Common Factor (GCF) of 72,30,409 By Common Division

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

Greatest Common Factor of 72,30,409 By Matching Biggest Common Factor Method

Now, list down the factors of 72

1,2,3,4,6,8,9,12,18,24,36,72

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 409

1,409

Greatest Common Factor

We found the factors 72,30,409 . The biggest common factor number is the GCF number.
So the greatest common factor 72,30,409 is 1.

Lets's calculate LCM of 35,40,13

Lowest Common Multiple of 35,40,13 using Common Division

5	35, 40, 13
	7, 8, 13

∴ So the LCM of the given numbers is 5 x 7 x 8 x 13 = 3640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3640

Therefore, the GCF of Fractions 72/35,30/40,409/13 is 1/3640

Least Common Multiple of 35,40,13 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 35,40,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(35,40,13) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(35,40,13) x common factors =1 x 5 = 5

LCM(35,40,13) = ( 35 × 40 × 13 ) / 5

LCM(35,40,13) = 18200 / 5

LCM(35,40,13) = 3640

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 72/35, 30/40, 409/13

1. What is the HCF of 72,30,409?

The HCF of 72,30,409 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 72/35, 30/40, 409/13?

Answer: GCF of Numerators as per given numbers 72/35, 30/40, 409/13 is

GCF of Numerators i.e. for 72,30,409 is 1

LCM of denominators i.e. for 35,40,13 is 3640.

Thus, GCF of Fractions is 1/3640.Finally, GCF of Fractions for 72/35, 30/40, 409/13 is 1/3640.