How to Find GCF of 42/54, 67/32, 278/320?

GCF of 42/54, 67/32, 278/320

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 42/54, 67/32, 278/320 i.e 1/8640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/54, 67/32, 278/320.

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 42/54,67/32,278/320?

Given fractions are 42/54,67/32,278/320

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 42/54,67/32,278/320, numerators are 42,67,278

Denominators are 54,32,320

The GCF of 42,67,278 is 1 .

LCM of 54,32,320 is 8640.

The greatest common factor of 42/54,67/32,278/320 = [GCF of 42,67,278]/[LCM of 54,32,320]= 1/8640

Therefore, the GCF of 42/54,67/32,278/320 is 1/8640.

Greatest Common Factor of 42,67,278

To find the highest common factor of 42,67,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 67 are 1, 67

The factors of 278 are 1, 2, 139, 278

The HCF of 42,67,278 is 1.

Lets's calculate GCF of 42,67,278

Greatest Common Factor (GCF) of 42,67,278 By Common Division

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

Greatest Common Factor of 42,67,278 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 67

1,67

Now, list down the factors of 278

1,2,139,278

Greatest Common Factor

We found the factors 42,67,278 . The biggest common factor number is the GCF number.
So the greatest common factor 42,67,278 is 1.

Lets's calculate LCM of 54,32,320

Lowest Common Multiple of 54,32,320 using Common Division

2	54, 32, 320
2	27, 16, 160
2	27, 8, 80
2	27, 4, 40
2	27, 2, 20
	27, 1, 10

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 27 x 1 x 10 = 8640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8640

Therefore, the GCF of Fractions 42/54,67/32,278/320 is 1/8640

Least Common Multiple of 54,32,320 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 54,32,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,32,320) = 2

common factors(in case of two or more numbers have common factors) = 32

GCF(54,32,320) x common factors =2 x 32 = 64

LCM(54,32,320) = ( 54 × 32 × 320 ) / 64

LCM(54,32,320) = 552960 / 64

LCM(54,32,320) = 8640

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 42/54, 67/32, 278/320

1. What is the HCF of 42,67,278?

The HCF of 42,67,278 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 42/54, 67/32, 278/320?

Answer: GCF of Numerators as per given numbers 42/54, 67/32, 278/320 is

GCF of Numerators i.e. for 42,67,278 is 1

LCM of denominators i.e. for 54,32,320 is 8640.

Thus, GCF of Fractions is 1/8640.Finally, GCF of Fractions for 42/54, 67/32, 278/320 is 1/8640.