How to Find GCF of 66/42, 10/61, 309/27?

GCF of 66/42, 10/61, 309/27

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 66/42, 10/61, 309/27 i.e 1/23058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/42, 10/61, 309/27.

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 66/42,10/61,309/27?

Given fractions are 66/42,10/61,309/27

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 66/42,10/61,309/27, numerators are 66,10,309

Denominators are 42,61,27

The GCF of 66,10,309 is 1 .

LCM of 42,61,27 is 23058.

The greatest common factor of 66/42,10/61,309/27 = [GCF of 66,10,309]/[LCM of 42,61,27]= 1/23058

Therefore, the GCF of 66/42,10/61,309/27 is 1/23058.

Greatest Common Factor of 66,10,309

To find the highest common factor of 66,10,309, we have to find the factors of both numbers and list the highest common factor.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 10 are 1, 2, 5, 10

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

The HCF of 66,10,309 is 1.

Lets's calculate GCF of 66,10,309

Greatest Common Factor (GCF) of 66,10,309 By Common Division

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

Greatest Common Factor of 66,10,309 By Matching Biggest Common Factor Method

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 309

1,3,103,309

Greatest Common Factor

We found the factors 66,10,309 . The biggest common factor number is the GCF number.
So the greatest common factor 66,10,309 is 1.

Lets's calculate LCM of 42,61,27

Lowest Common Multiple of 42,61,27 using Common Division

3	42, 61, 27
	14, 61, 9

∴ So the LCM of the given numbers is 3 x 14 x 61 x 9 = 23058

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23058

Therefore, the GCF of Fractions 66/42,10/61,309/27 is 1/23058

Least Common Multiple of 42,61,27 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 42,61,27 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,61,27) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(42,61,27) x common factors =1 x 3 = 3

LCM(42,61,27) = ( 42 × 61 × 27 ) / 3

LCM(42,61,27) = 69174 / 3

LCM(42,61,27) = 23058

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 66/42, 10/61, 309/27

1. What is the HCF of 66,10,309?

The HCF of 66,10,309 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 66/42, 10/61, 309/27?

Answer: GCF of Numerators as per given numbers 66/42, 10/61, 309/27 is

GCF of Numerators i.e. for 66,10,309 is 1

LCM of denominators i.e. for 42,61,27 is 23058.

Thus, GCF of Fractions is 1/23058.Finally, GCF of Fractions for 66/42, 10/61, 309/27 is 1/23058.