How to Find GCF of 54/60, 29/49, 414/794?

GCF of 54/60, 29/49, 414/794

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 54/60, 29/49, 414/794 i.e 1/1167180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/60, 29/49, 414/794.

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 54/60,29/49,414/794?

Given fractions are 54/60,29/49,414/794

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 54/60,29/49,414/794, numerators are 54,29,414

Denominators are 60,49,794

The GCF of 54,29,414 is 1 .

LCM of 60,49,794 is 1167180.

The greatest common factor of 54/60,29/49,414/794 = [GCF of 54,29,414]/[LCM of 60,49,794]= 1/1167180

Therefore, the GCF of 54/60,29/49,414/794 is 1/1167180.

Greatest Common Factor of 54,29,414

To find the highest common factor of 54,29,414, we have to find the factors of both numbers and list the highest common factor.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 29 are 1, 29

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 54,29,414 is 1.

Lets's calculate GCF of 54,29,414

Greatest Common Factor (GCF) of 54,29,414 By Common Division

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

Greatest Common Factor of 54,29,414 By Matching Biggest Common Factor Method

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 29

1,29

Now, list down the factors of 414

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 54,29,414 . The biggest common factor number is the GCF number.
So the greatest common factor 54,29,414 is 1.

Lets's calculate LCM of 60,49,794

Lowest Common Multiple of 60,49,794 using Common Division

2	60, 49, 794
	30, 49, 397

∴ So the LCM of the given numbers is 2 x 30 x 49 x 397 = 1167180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1167180

Therefore, the GCF of Fractions 54/60,29/49,414/794 is 1/1167180

Least Common Multiple of 60,49,794 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 60,49,794 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(60,49,794) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(60,49,794) x common factors =1 x 2 = 2

LCM(60,49,794) = ( 60 × 49 × 794 ) / 2

LCM(60,49,794) = 2334360 / 2

LCM(60,49,794) = 1167180

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FAQs on GCF of Fractions of 54/60, 29/49, 414/794

1. What is the HCF of 54,29,414?

The HCF of 54,29,414 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 54/60, 29/49, 414/794?

Answer: GCF of Numerators as per given numbers 54/60, 29/49, 414/794 is

GCF of Numerators i.e. for 54,29,414 is 1

LCM of denominators i.e. for 60,49,794 is 1167180.

Thus, GCF of Fractions is 1/1167180.Finally, GCF of Fractions for 54/60, 29/49, 414/794 is 1/1167180.