How to Find GCF of 666/11, 540/786?

GCF of 666/11, 540/786

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 666/11, 540/786 i.e 18/8646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 666/11, 540/786.

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 666/11,540/786?

Given fractions are 666/11,540/786

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 666/11,540/786, numerators are 666,540

Denominators are 11,786

The GCF of 666,540 is 18 .

LCM of 11,786 is 8646.

The greatest common factor of 666/11,540/786 = [GCF of 666,540]/[LCM of 11,786]= 18/8646

Therefore, the GCF of 666/11,540/786 is 18/8646.

Greatest Common Factor of 666,540

To find the highest common factor of 666,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 666,540 is 18.

Lets's calculate GCF of 666,540

Greatest Common Factor (GCF) of 666,540 By Common Division

2	666, 540
3	333, 270
3	111, 90
	37, 30

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 666,540 By Matching Biggest Common Factor Method

Now, list down the factors of 666

1,2,3,6,9,18,37,74,111,222,333,666

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 666,540 . The biggest common factor number is the GCF number.
So the greatest common factor 666,540 is 18.

Lets's calculate LCM of 11,786

Lowest Common Multiple of 11,786 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 8646

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/8646

Therefore, the GCF of Fractions 666/11,540/786 is 18/8646

Least Common Multiple of 11,786 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 11,786 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(11,786) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(11,786) x common factors =1 x 1 = 1

LCM(11,786) = ( 11 × 786 ) / 1

LCM(11,786) = 8646 / 1

LCM(11,786) = 8646

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FAQs on GCF of Fractions of 666/11, 540/786

1. What is the HCF of 666,540?

The HCF of 666,540 is 18

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 666/11, 540/786?

Answer: GCF of Numerators as per given numbers 666/11, 540/786 is

GCF of Numerators i.e. for 666,540 is 18

LCM of denominators i.e. for 11,786 is 8646.

Thus, GCF of Fractions is 18/8646.Finally, GCF of Fractions for 666/11, 540/786 is 18/8646.