How to Find GCF of 78/54, 21/60, 65/57?

GCF of 78/54, 21/60, 65/57

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 78/54, 21/60, 65/57 i.e 1/10260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/54, 21/60, 65/57.

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 78/54,21/60,65/57?

Given fractions are 78/54,21/60,65/57

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 78/54,21/60,65/57, numerators are 78,21,65

Denominators are 54,60,57

The GCF of 78,21,65 is 1 .

LCM of 54,60,57 is 10260.

The greatest common factor of 78/54,21/60,65/57 = [GCF of 78,21,65]/[LCM of 54,60,57]= 1/10260

Therefore, the GCF of 78/54,21/60,65/57 is 1/10260.

Greatest Common Factor of 78,21,65

To find the highest common factor of 78,21,65, we have to find the factors of both numbers and list the highest common factor.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 21 are 1, 3, 7, 21

The factors of 65 are 1, 5, 13, 65

The HCF of 78,21,65 is 1.

Lets's calculate GCF of 78,21,65

Greatest Common Factor (GCF) of 78,21,65 By Common Division

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

Greatest Common Factor of 78,21,65 By Matching Biggest Common Factor Method

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 65

1,5,13,65

Greatest Common Factor

We found the factors 78,21,65 . The biggest common factor number is the GCF number.
So the greatest common factor 78,21,65 is 1.

Lets's calculate LCM of 54,60,57

Lowest Common Multiple of 54,60,57 using Common Division

2	54, 60, 57
3	27, 30, 57
	9, 10, 19

∴ So the LCM of the given numbers is 2 x 3 x 9 x 10 x 19 = 10260

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10260

Therefore, the GCF of Fractions 78/54,21/60,65/57 is 1/10260

Least Common Multiple of 54,60,57 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 54,60,57 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,60,57) = 3

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

GCF(54,60,57) x common factors =3 x 6 = 18

LCM(54,60,57) = ( 54 × 60 × 57 ) / 18

LCM(54,60,57) = 184680 / 18

LCM(54,60,57) = 10260

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FAQs on GCF of Fractions of 78/54, 21/60, 65/57

1. What is the HCF of 78,21,65?

The HCF of 78,21,65 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 78/54, 21/60, 65/57?

Answer: GCF of Numerators as per given numbers 78/54, 21/60, 65/57 is

GCF of Numerators i.e. for 78,21,65 is 1

LCM of denominators i.e. for 54,60,57 is 10260.

Thus, GCF of Fractions is 1/10260.Finally, GCF of Fractions for 78/54, 21/60, 65/57 is 1/10260.