How to Find GCF of 25/27, 54/68, 238/64?

GCF of 25/27, 54/68, 238/64

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 25/27, 54/68, 238/64 i.e 1/29376 easily. The following is the detailed procedure to determine the greatest common factor of fractions 25/27, 54/68, 238/64.

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 25/27,54/68,238/64?

Given fractions are 25/27,54/68,238/64

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 25/27,54/68,238/64, numerators are 25,54,238

Denominators are 27,68,64

The GCF of 25,54,238 is 1 .

LCM of 27,68,64 is 29376.

The greatest common factor of 25/27,54/68,238/64 = [GCF of 25,54,238]/[LCM of 27,68,64]= 1/29376

Therefore, the GCF of 25/27,54/68,238/64 is 1/29376.

Greatest Common Factor of 25,54,238

To find the highest common factor of 25,54,238, we have to find the factors of both numbers and list the highest common factor.

The factors of 25 are 1, 5, 25

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238

The HCF of 25,54,238 is 1.

Lets's calculate GCF of 25,54,238

Greatest Common Factor (GCF) of 25,54,238 By Common Division

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

Greatest Common Factor of 25,54,238 By Matching Biggest Common Factor Method

Now, list down the factors of 25

1,5,25

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 238

1,2,7,14,17,34,119,238

Greatest Common Factor

We found the factors 25,54,238 . The biggest common factor number is the GCF number.
So the greatest common factor 25,54,238 is 1.

Lets's calculate LCM of 27,68,64

Lowest Common Multiple of 27,68,64 using Common Division

2	27, 68, 64
2	27, 34, 32
	27, 17, 16

∴ So the LCM of the given numbers is 2 x 2 x 27 x 17 x 16 = 29376

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29376

Therefore, the GCF of Fractions 25/27,54/68,238/64 is 1/29376

Least Common Multiple of 27,68,64 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 27,68,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,68,64) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(27,68,64) x common factors =1 x 4 = 4

LCM(27,68,64) = ( 27 × 68 × 64 ) / 4

LCM(27,68,64) = 117504 / 4

LCM(27,68,64) = 29376

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 25/27, 54/68, 238/64

1. What is the HCF of 25,54,238?

The HCF of 25,54,238 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 25/27, 54/68, 238/64?

Answer: GCF of Numerators as per given numbers 25/27, 54/68, 238/64 is

GCF of Numerators i.e. for 25,54,238 is 1

LCM of denominators i.e. for 27,68,64 is 29376.

Thus, GCF of Fractions is 1/29376.Finally, GCF of Fractions for 25/27, 54/68, 238/64 is 1/29376.