How to Find GCF of 54/28, 85/150, 421/142?

GCF of 54/28, 85/150, 421/142

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 54/28, 85/150, 421/142 i.e 1/149100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/28, 85/150, 421/142.

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 54/28,85/150,421/142?

Given fractions are 54/28,85/150,421/142

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 54/28,85/150,421/142, numerators are 54,85,421

Denominators are 28,150,142

The GCF of 54,85,421 is 1 .

LCM of 28,150,142 is 149100.

The greatest common factor of 54/28,85/150,421/142 = [GCF of 54,85,421]/[LCM of 28,150,142]= 1/149100

Therefore, the GCF of 54/28,85/150,421/142 is 1/149100.

Greatest Common Factor of 54,85,421

To find the highest common factor of 54,85,421, 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 85 are 1, 5, 17, 85

The factors of 421 are 1, 421

The HCF of 54,85,421 is 1.

Lets's calculate GCF of 54,85,421

Greatest Common Factor (GCF) of 54,85,421 By Common Division

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

Greatest Common Factor of 54,85,421 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 85

1,5,17,85

Now, list down the factors of 421

1,421

Greatest Common Factor

We found the factors 54,85,421 . The biggest common factor number is the GCF number.
So the greatest common factor 54,85,421 is 1.

Lets's calculate LCM of 28,150,142

Lowest Common Multiple of 28,150,142 using Common Division

2	28, 150, 142
	14, 75, 71

∴ So the LCM of the given numbers is 2 x 14 x 75 x 71 = 149100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/149100

Therefore, the GCF of Fractions 54/28,85/150,421/142 is 1/149100

Least Common Multiple of 28,150,142 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 28,150,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,150,142) = 2

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

GCF(28,150,142) x common factors =2 x 2 = 4

LCM(28,150,142) = ( 28 × 150 × 142 ) / 4

LCM(28,150,142) = 596400 / 4

LCM(28,150,142) = 149100

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FAQs on GCF of Fractions of 54/28, 85/150, 421/142

1. What is the HCF of 54,85,421?

The HCF of 54,85,421 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 54/28, 85/150, 421/142?

Answer: GCF of Numerators as per given numbers 54/28, 85/150, 421/142 is

GCF of Numerators i.e. for 54,85,421 is 1

LCM of denominators i.e. for 28,150,142 is 149100.

Thus, GCF of Fractions is 1/149100.Finally, GCF of Fractions for 54/28, 85/150, 421/142 is 1/149100.