How to Find GCF of 65/69, 81/14, 13/218?

GCF of 65/69, 81/14, 13/218

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 65/69, 81/14, 13/218 i.e 1/105294 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/69, 81/14, 13/218.

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 65/69,81/14,13/218?

Given fractions are 65/69,81/14,13/218

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 65/69,81/14,13/218, numerators are 65,81,13

Denominators are 69,14,218

The GCF of 65,81,13 is 1 .

LCM of 69,14,218 is 105294.

The greatest common factor of 65/69,81/14,13/218 = [GCF of 65,81,13]/[LCM of 69,14,218]= 1/105294

Therefore, the GCF of 65/69,81/14,13/218 is 1/105294.

Greatest Common Factor of 65,81,13

To find the highest common factor of 65,81,13, we have to find the factors of both numbers and list the highest common factor.

The factors of 65 are 1, 5, 13, 65

The factors of 81 are 1, 3, 9, 27, 81

The factors of 13 are 1, 13

The HCF of 65,81,13 is 1.

Lets's calculate GCF of 65,81,13

Greatest Common Factor (GCF) of 65,81,13 By Common Division

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

Greatest Common Factor of 65,81,13 By Matching Biggest Common Factor Method

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 81

1,3,9,27,81

Now, list down the factors of 13

1,13

Greatest Common Factor

We found the factors 65,81,13 . The biggest common factor number is the GCF number.
So the greatest common factor 65,81,13 is 1.

Lets's calculate LCM of 69,14,218

Lowest Common Multiple of 69,14,218 using Common Division

2	69, 14, 218
	69, 7, 109

∴ So the LCM of the given numbers is 2 x 69 x 7 x 109 = 105294

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105294

Therefore, the GCF of Fractions 65/69,81/14,13/218 is 1/105294

Least Common Multiple of 69,14,218 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 69,14,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,14,218) = 1

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

GCF(69,14,218) x common factors =1 x 2 = 2

LCM(69,14,218) = ( 69 × 14 × 218 ) / 2

LCM(69,14,218) = 210588 / 2

LCM(69,14,218) = 105294

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FAQs on GCF of Fractions of 65/69, 81/14, 13/218

1. What is the HCF of 65,81,13?

The HCF of 65,81,13 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 65/69, 81/14, 13/218?

Answer: GCF of Numerators as per given numbers 65/69, 81/14, 13/218 is

GCF of Numerators i.e. for 65,81,13 is 1

LCM of denominators i.e. for 69,14,218 is 105294.

Thus, GCF of Fractions is 1/105294.Finally, GCF of Fractions for 65/69, 81/14, 13/218 is 1/105294.