How to Find GCF of 13/78, 45/96, 277/818?

GCF of 13/78, 45/96, 277/818

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 13/78, 45/96, 277/818 i.e 1/510432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/78, 45/96, 277/818.

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 13/78,45/96,277/818?

Given fractions are 13/78,45/96,277/818

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 13/78,45/96,277/818, numerators are 13,45,277

Denominators are 78,96,818

The GCF of 13,45,277 is 1 .

LCM of 78,96,818 is 510432.

The greatest common factor of 13/78,45/96,277/818 = [GCF of 13,45,277]/[LCM of 78,96,818]= 1/510432

Therefore, the GCF of 13/78,45/96,277/818 is 1/510432.

Greatest Common Factor of 13,45,277

To find the highest common factor of 13,45,277, 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 45 are 1, 3, 5, 9, 15, 45

The factors of 277 are 1, 277

The HCF of 13,45,277 is 1.

Lets's calculate GCF of 13,45,277

Greatest Common Factor (GCF) of 13,45,277 By Common Division

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

Greatest Common Factor of 13,45,277 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 45

1,3,5,9,15,45

Now, list down the factors of 277

1,277

Greatest Common Factor

We found the factors 13,45,277 . The biggest common factor number is the GCF number.
So the greatest common factor 13,45,277 is 1.

Lets's calculate LCM of 78,96,818

Lowest Common Multiple of 78,96,818 using Common Division

2	78, 96, 818
3	39, 48, 409
	13, 16, 409

∴ So the LCM of the given numbers is 2 x 3 x 13 x 16 x 409 = 510432

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/510432

Therefore, the GCF of Fractions 13/78,45/96,277/818 is 1/510432

Least Common Multiple of 78,96,818 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 78,96,818 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,96,818) = 2

common factors(in case of two or more numbers have common factors) = 6

GCF(78,96,818) x common factors =2 x 6 = 12

LCM(78,96,818) = ( 78 × 96 × 818 ) / 12

LCM(78,96,818) = 6125184 / 12

LCM(78,96,818) = 510432

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FAQs on GCF of Fractions of 13/78, 45/96, 277/818

1. What is the HCF of 13,45,277?

The HCF of 13,45,277 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 13/78, 45/96, 277/818?

Answer: GCF of Numerators as per given numbers 13/78, 45/96, 277/818 is

GCF of Numerators i.e. for 13,45,277 is 1

LCM of denominators i.e. for 78,96,818 is 510432.

Thus, GCF of Fractions is 1/510432.Finally, GCF of Fractions for 13/78, 45/96, 277/818 is 1/510432.