How to Find GCF of 69/13, 21/82, 52/86, 22/16?

GCF of 69/13, 21/82, 52/86, 22/16

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 69/13, 21/82, 52/86, 22/16 i.e 1/366704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/13, 21/82, 52/86, 22/16.

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 69/13,21/82,52/86,22/16?

Given fractions are 69/13,21/82,52/86,22/16

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 69/13,21/82,52/86,22/16, numerators are 69,21,52,22

Denominators are 13,82,86,16

The GCF of 69,21,52,22 is 1 .

LCM of 13,82,86,16 is 366704.

The greatest common factor of 69/13,21/82,52/86,22/16 = [GCF of 69,21,52,22]/[LCM of 13,82,86,16]= 1/366704

Therefore, the GCF of 69/13,21/82,52/86,22/16 is 1/366704.

Greatest Common Factor of 69,21,52,22

To find the highest common factor of 69,21,52,22, we have to find the factors of both numbers and list the highest common factor.

The factors of 69 are 1, 3, 23, 69

The factors of 21 are 1, 3, 7, 21

The factors of 52 are 1, 2, 4, 13, 26, 52

The factors of 22 are 1, 2, 11, 22

The HCF of 69,21,52,22 is 1.

Lets's calculate GCF of 69,21,52,22

Greatest Common Factor (GCF) of 69,21,52,22 By Common Division

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

Greatest Common Factor of 69,21,52,22 By Matching Biggest Common Factor Method

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 52

1,2,4,13,26,52

Now, list down the factors of 22

1,2,11,22

Greatest Common Factor

We found the factors 69,21,52,22 . The biggest common factor number is the GCF number.
So the greatest common factor 69,21,52,22 is 1.

Lets's calculate LCM of 13,82,86,16

Lowest Common Multiple of 13,82,86,16 using Common Division

2	13, 82, 86, 16
	13, 41, 43, 8

∴ So the LCM of the given numbers is 2 x 13 x 41 x 43 x 8 = 366704

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/366704

Therefore, the GCF of Fractions 69/13,21/82,52/86,22/16 is 1/366704

Least Common Multiple of 13,82,86,16 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 13,82,86,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,82,86,16) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(13,82,86,16) x common factors =1 x 4 = 4

LCM(13,82,86,16) = ( 13 × 82 × 86 × 16 ) / 4

LCM(13,82,86,16) = 1466816 / 4

LCM(13,82,86,16) = 366704

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 69/13, 21/82, 52/86, 22/16

1. What is the HCF of 69,21,52,22?

The HCF of 69,21,52,22 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 69/13, 21/82, 52/86, 22/16?

Answer: GCF of Numerators as per given numbers 69/13, 21/82, 52/86, 22/16 is

GCF of Numerators i.e. for 69,21,52,22 is 1

LCM of denominators i.e. for 13,82,86,16 is 366704.

Thus, GCF of Fractions is 1/366704.Finally, GCF of Fractions for 69/13, 21/82, 52/86, 22/16 is 1/366704.