How to Find GCF of 301/46, 587/29, 713/16?

GCF of 301/46, 587/29, 713/16

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 301/46, 587/29, 713/16 i.e 1/10672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 301/46, 587/29, 713/16.

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 301/46,587/29,713/16?

Given fractions are 301/46,587/29,713/16

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 301/46,587/29,713/16, numerators are 301,587,713

Denominators are 46,29,16

The GCF of 301,587,713 is 1 .

LCM of 46,29,16 is 10672.

The greatest common factor of 301/46,587/29,713/16 = [GCF of 301,587,713]/[LCM of 46,29,16]= 1/10672

Therefore, the GCF of 301/46,587/29,713/16 is 1/10672.

Greatest Common Factor of 301,587,713

To find the highest common factor of 301,587,713, we have to find the factors of both numbers and list the highest common factor.

The factors of 301 are 1, 7, 43, 301

The factors of 587 are 1, 587

The factors of 713 are 1, 23, 31, 713

The HCF of 301,587,713 is 1.

Lets's calculate GCF of 301,587,713

Greatest Common Factor (GCF) of 301,587,713 By Common Division

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

Greatest Common Factor of 301,587,713 By Matching Biggest Common Factor Method

Now, list down the factors of 301

1,7,43,301

Now, list down the factors of 587

1,587

Now, list down the factors of 713

1,23,31,713

Greatest Common Factor

We found the factors 301,587,713 . The biggest common factor number is the GCF number.
So the greatest common factor 301,587,713 is 1.

Lets's calculate LCM of 46,29,16

Lowest Common Multiple of 46,29,16 using Common Division

2	46, 29, 16
	23, 29, 8

∴ So the LCM of the given numbers is 2 x 23 x 29 x 8 = 10672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10672

Therefore, the GCF of Fractions 301/46,587/29,713/16 is 1/10672

Least Common Multiple of 46,29,16 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 46,29,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(46,29,16) = 1

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

GCF(46,29,16) x common factors =1 x 2 = 2

LCM(46,29,16) = ( 46 × 29 × 16 ) / 2

LCM(46,29,16) = 21344 / 2

LCM(46,29,16) = 10672

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FAQs on GCF of Fractions of 301/46, 587/29, 713/16

1. What is the HCF of 301,587,713?

The HCF of 301,587,713 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 301/46, 587/29, 713/16?

Answer: GCF of Numerators as per given numbers 301/46, 587/29, 713/16 is

GCF of Numerators i.e. for 301,587,713 is 1

LCM of denominators i.e. for 46,29,16 is 10672.

Thus, GCF of Fractions is 1/10672.Finally, GCF of Fractions for 301/46, 587/29, 713/16 is 1/10672.