How to Find GCF of 17/41, 64/40, 541/38?

GCF of 17/41, 64/40, 541/38

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 17/41, 64/40, 541/38 i.e 1/31160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/41, 64/40, 541/38.

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 17/41,64/40,541/38?

Given fractions are 17/41,64/40,541/38

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 17/41,64/40,541/38, numerators are 17,64,541

Denominators are 41,40,38

The GCF of 17,64,541 is 1 .

LCM of 41,40,38 is 31160.

The greatest common factor of 17/41,64/40,541/38 = [GCF of 17,64,541]/[LCM of 41,40,38]= 1/31160

Therefore, the GCF of 17/41,64/40,541/38 is 1/31160.

Greatest Common Factor of 17,64,541

To find the highest common factor of 17,64,541, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 64 are 1, 2, 4, 8, 16, 32, 64

The factors of 541 are 1, 541

The HCF of 17,64,541 is 1.

Lets's calculate GCF of 17,64,541

Greatest Common Factor (GCF) of 17,64,541 By Common Division

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

Greatest Common Factor of 17,64,541 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 64

1,2,4,8,16,32,64

Now, list down the factors of 541

1,541

Greatest Common Factor

We found the factors 17,64,541 . The biggest common factor number is the GCF number.
So the greatest common factor 17,64,541 is 1.

Lets's calculate LCM of 41,40,38

Lowest Common Multiple of 41,40,38 using Common Division

2	41, 40, 38
	41, 20, 19

∴ So the LCM of the given numbers is 2 x 41 x 20 x 19 = 31160

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31160

Therefore, the GCF of Fractions 17/41,64/40,541/38 is 1/31160

Least Common Multiple of 41,40,38 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 41,40,38 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(41,40,38) = 1

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

GCF(41,40,38) x common factors =1 x 2 = 2

LCM(41,40,38) = ( 41 × 40 × 38 ) / 2

LCM(41,40,38) = 62320 / 2

LCM(41,40,38) = 31160

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/41, 64/40, 541/38

1. What is the HCF of 17,64,541?

The HCF of 17,64,541 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 17/41, 64/40, 541/38?

Answer: GCF of Numerators as per given numbers 17/41, 64/40, 541/38 is

GCF of Numerators i.e. for 17,64,541 is 1

LCM of denominators i.e. for 41,40,38 is 31160.

Thus, GCF of Fractions is 1/31160.Finally, GCF of Fractions for 17/41, 64/40, 541/38 is 1/31160.