How to Find GCF of 14/74, 71/47, 278/16?

GCF of 14/74, 71/47, 278/16

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 14/74, 71/47, 278/16 i.e 1/27824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/74, 71/47, 278/16.

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 14/74,71/47,278/16?

Given fractions are 14/74,71/47,278/16

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 14/74,71/47,278/16, numerators are 14,71,278

Denominators are 74,47,16

The GCF of 14,71,278 is 1 .

LCM of 74,47,16 is 27824.

The greatest common factor of 14/74,71/47,278/16 = [GCF of 14,71,278]/[LCM of 74,47,16]= 1/27824

Therefore, the GCF of 14/74,71/47,278/16 is 1/27824.

Greatest Common Factor of 14,71,278

To find the highest common factor of 14,71,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 71 are 1, 71

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

The HCF of 14,71,278 is 1.

Lets's calculate GCF of 14,71,278

Greatest Common Factor (GCF) of 14,71,278 By Common Division

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

Greatest Common Factor of 14,71,278 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 71

1,71

Now, list down the factors of 278

1,2,139,278

Greatest Common Factor

We found the factors 14,71,278 . The biggest common factor number is the GCF number.
So the greatest common factor 14,71,278 is 1.

Lets's calculate LCM of 74,47,16

Lowest Common Multiple of 74,47,16 using Common Division

2	74, 47, 16
	37, 47, 8

∴ So the LCM of the given numbers is 2 x 37 x 47 x 8 = 27824

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27824

Therefore, the GCF of Fractions 14/74,71/47,278/16 is 1/27824

Least Common Multiple of 74,47,16 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 74,47,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,47,16) = 1

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

GCF(74,47,16) x common factors =1 x 2 = 2

LCM(74,47,16) = ( 74 × 47 × 16 ) / 2

LCM(74,47,16) = 55648 / 2

LCM(74,47,16) = 27824

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FAQs on GCF of Fractions of 14/74, 71/47, 278/16

1. What is the HCF of 14,71,278?

The HCF of 14,71,278 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 14/74, 71/47, 278/16?

Answer: GCF of Numerators as per given numbers 14/74, 71/47, 278/16 is

GCF of Numerators i.e. for 14,71,278 is 1

LCM of denominators i.e. for 74,47,16 is 27824.

Thus, GCF of Fractions is 1/27824.Finally, GCF of Fractions for 14/74, 71/47, 278/16 is 1/27824.