How to Find GCF of 809/46, 610/90, 108/36?

GCF of 809/46, 610/90, 108/36

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 809/46, 610/90, 108/36 i.e 1/4140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 809/46, 610/90, 108/36.

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 809/46,610/90,108/36?

Given fractions are 809/46,610/90,108/36

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 809/46,610/90,108/36, numerators are 809,610,108

Denominators are 46,90,36

The GCF of 809,610,108 is 1 .

LCM of 46,90,36 is 4140.

The greatest common factor of 809/46,610/90,108/36 = [GCF of 809,610,108]/[LCM of 46,90,36]= 1/4140

Therefore, the GCF of 809/46,610/90,108/36 is 1/4140.

Greatest Common Factor of 809,610,108

To find the highest common factor of 809,610,108, we have to find the factors of both numbers and list the highest common factor.

The factors of 809 are 1, 809

The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The HCF of 809,610,108 is 1.

Lets's calculate GCF of 809,610,108

Greatest Common Factor (GCF) of 809,610,108 By Common Division

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

Greatest Common Factor of 809,610,108 By Matching Biggest Common Factor Method

Now, list down the factors of 809

1,809

Now, list down the factors of 610

1,2,5,10,61,122,305,610

Now, list down the factors of 108

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors 809,610,108 . The biggest common factor number is the GCF number.
So the greatest common factor 809,610,108 is 1.

Lets's calculate LCM of 46,90,36

Lowest Common Multiple of 46,90,36 using Common Division

2	46, 90, 36
3	23, 45, 18
3	23, 15, 6
	23, 5, 2

∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 5 x 2 = 4140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4140

Therefore, the GCF of Fractions 809/46,610/90,108/36 is 1/4140

Least Common Multiple of 46,90,36 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 46,90,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(46,90,36) = 2

common factors(in case of two or more numbers have common factors) = 18

GCF(46,90,36) x common factors =2 x 18 = 36

LCM(46,90,36) = ( 46 × 90 × 36 ) / 36

LCM(46,90,36) = 149040 / 36

LCM(46,90,36) = 4140

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FAQs on GCF of Fractions of 809/46, 610/90, 108/36

1. What is the HCF of 809,610,108?

The HCF of 809,610,108 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 809/46, 610/90, 108/36?

Answer: GCF of Numerators as per given numbers 809/46, 610/90, 108/36 is

GCF of Numerators i.e. for 809,610,108 is 1

LCM of denominators i.e. for 46,90,36 is 4140.

Thus, GCF of Fractions is 1/4140.Finally, GCF of Fractions for 809/46, 610/90, 108/36 is 1/4140.