How to Find GCF of 13/229, 76/240, 307/540?

GCF of 13/229, 76/240, 307/540

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 13/229, 76/240, 307/540 i.e 1/494640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/229, 76/240, 307/540.

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 13/229,76/240,307/540?

Given fractions are 13/229,76/240,307/540

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 13/229,76/240,307/540, numerators are 13,76,307

Denominators are 229,240,540

The GCF of 13,76,307 is 1 .

LCM of 229,240,540 is 494640.

The greatest common factor of 13/229,76/240,307/540 = [GCF of 13,76,307]/[LCM of 229,240,540]= 1/494640

Therefore, the GCF of 13/229,76/240,307/540 is 1/494640.

Greatest Common Factor of 13,76,307

To find the highest common factor of 13,76,307, we have to find the factors of both numbers and list the highest common factor.

The factors of 13 are 1, 13

The factors of 76 are 1, 2, 4, 19, 38, 76

The factors of 307 are 1, 307

The HCF of 13,76,307 is 1.

Lets's calculate GCF of 13,76,307

Greatest Common Factor (GCF) of 13,76,307 By Common Division

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

Greatest Common Factor of 13,76,307 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 76

1,2,4,19,38,76

Now, list down the factors of 307

1,307

Greatest Common Factor

We found the factors 13,76,307 . The biggest common factor number is the GCF number.
So the greatest common factor 13,76,307 is 1.

Lets's calculate LCM of 229,240,540

Lowest Common Multiple of 229,240,540 using Common Division

2	229, 240, 540
2	229, 120, 270
3	229, 60, 135
5	229, 20, 45
	229, 4, 9

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 229 x 4 x 9 = 494640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/494640

Therefore, the GCF of Fractions 13/229,76/240,307/540 is 1/494640

Least Common Multiple of 229,240,540 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 229,240,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(229,240,540) = 1

common factors(in case of two or more numbers have common factors) = 60

GCF(229,240,540) x common factors =1 x 60 = 60

LCM(229,240,540) = ( 229 × 240 × 540 ) / 60

LCM(229,240,540) = 29678400 / 60

LCM(229,240,540) = 494640

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 13/229, 76/240, 307/540

1. What is the HCF of 13,76,307?

The HCF of 13,76,307 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 13/229, 76/240, 307/540?

Answer: GCF of Numerators as per given numbers 13/229, 76/240, 307/540 is

GCF of Numerators i.e. for 13,76,307 is 1

LCM of denominators i.e. for 229,240,540 is 494640.

Thus, GCF of Fractions is 1/494640.Finally, GCF of Fractions for 13/229, 76/240, 307/540 is 1/494640.