How to Find GCF of 27/16, 309/12, 323/258?

GCF of 27/16, 309/12, 323/258

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 27/16, 309/12, 323/258 i.e 1/2064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/16, 309/12, 323/258.

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 27/16,309/12,323/258?

Given fractions are 27/16,309/12,323/258

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 27/16,309/12,323/258, numerators are 27,309,323

Denominators are 16,12,258

The GCF of 27,309,323 is 1 .

LCM of 16,12,258 is 2064.

The greatest common factor of 27/16,309/12,323/258 = [GCF of 27,309,323]/[LCM of 16,12,258]= 1/2064

Therefore, the GCF of 27/16,309/12,323/258 is 1/2064.

Greatest Common Factor of 27,309,323

To find the highest common factor of 27,309,323, we have to find the factors of both numbers and list the highest common factor.

The factors of 27 are 1, 3, 9, 27

The factors of 309 are 1, 3, 103, 309

The factors of 323 are 1, 17, 19, 323

The HCF of 27,309,323 is 1.

Lets's calculate GCF of 27,309,323

Greatest Common Factor (GCF) of 27,309,323 By Common Division

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

Greatest Common Factor of 27,309,323 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 309

1,3,103,309

Now, list down the factors of 323

1,17,19,323

Greatest Common Factor

We found the factors 27,309,323 . The biggest common factor number is the GCF number.
So the greatest common factor 27,309,323 is 1.

Lets's calculate LCM of 16,12,258

Lowest Common Multiple of 16,12,258 using Common Division

2	16, 12, 258
2	8, 6, 129
3	4, 3, 129
	4, 1, 43

∴ So the LCM of the given numbers is 2 x 2 x 3 x 4 x 1 x 43 = 2064

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2064

Therefore, the GCF of Fractions 27/16,309/12,323/258 is 1/2064

Least Common Multiple of 16,12,258 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 16,12,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,12,258) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(16,12,258) x common factors =2 x 12 = 24

LCM(16,12,258) = ( 16 × 12 × 258 ) / 24

LCM(16,12,258) = 49536 / 24

LCM(16,12,258) = 2064

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FAQs on GCF of Fractions of 27/16, 309/12, 323/258

1. What is the HCF of 27,309,323?

The HCF of 27,309,323 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 27/16, 309/12, 323/258?

Answer: GCF of Numerators as per given numbers 27/16, 309/12, 323/258 is

GCF of Numerators i.e. for 27,309,323 is 1

LCM of denominators i.e. for 16,12,258 is 2064.

Thus, GCF of Fractions is 1/2064.Finally, GCF of Fractions for 27/16, 309/12, 323/258 is 1/2064.