How to Find GCF of 209/43, 545/96, 811/64?

GCF of 209/43, 545/96, 811/64

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 209/43, 545/96, 811/64 i.e 1/8256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/43, 545/96, 811/64.

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 209/43,545/96,811/64?

Given fractions are 209/43,545/96,811/64

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 209/43,545/96,811/64, numerators are 209,545,811

Denominators are 43,96,64

The GCF of 209,545,811 is 1 .

LCM of 43,96,64 is 8256.

The greatest common factor of 209/43,545/96,811/64 = [GCF of 209,545,811]/[LCM of 43,96,64]= 1/8256

Therefore, the GCF of 209/43,545/96,811/64 is 1/8256.

Greatest Common Factor of 209,545,811

To find the highest common factor of 209,545,811, we have to find the factors of both numbers and list the highest common factor.

The factors of 209 are 1, 11, 19, 209

The factors of 545 are 1, 5, 109, 545

The factors of 811 are 1, 811

The HCF of 209,545,811 is 1.

Lets's calculate GCF of 209,545,811

Greatest Common Factor (GCF) of 209,545,811 By Common Division

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

Greatest Common Factor of 209,545,811 By Matching Biggest Common Factor Method

Now, list down the factors of 209

1,11,19,209

Now, list down the factors of 545

1,5,109,545

Now, list down the factors of 811

1,811

Greatest Common Factor

We found the factors 209,545,811 . The biggest common factor number is the GCF number.
So the greatest common factor 209,545,811 is 1.

Lets's calculate LCM of 43,96,64

Lowest Common Multiple of 43,96,64 using Common Division

2	43, 96, 64
2	43, 48, 32
2	43, 24, 16
2	43, 12, 8
2	43, 6, 4
	43, 3, 2

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 43 x 3 x 2 = 8256

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8256

Therefore, the GCF of Fractions 209/43,545/96,811/64 is 1/8256

Least Common Multiple of 43,96,64 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 43,96,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(43,96,64) = 1

common factors(in case of two or more numbers have common factors) = 32

GCF(43,96,64) x common factors =1 x 32 = 32

LCM(43,96,64) = ( 43 × 96 × 64 ) / 32

LCM(43,96,64) = 264192 / 32

LCM(43,96,64) = 8256

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 209/43, 545/96, 811/64

1. What is the HCF of 209,545,811?

The HCF of 209,545,811 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 209/43, 545/96, 811/64?

Answer: GCF of Numerators as per given numbers 209/43, 545/96, 811/64 is

GCF of Numerators i.e. for 209,545,811 is 1

LCM of denominators i.e. for 43,96,64 is 8256.

Thus, GCF of Fractions is 1/8256.Finally, GCF of Fractions for 209/43, 545/96, 811/64 is 1/8256.