How to Find GCF of 73/130, 36/109, 969/500?

GCF of 73/130, 36/109, 969/500

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 73/130, 36/109, 969/500 i.e 1/708500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 73/130, 36/109, 969/500.

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 73/130,36/109,969/500?

Given fractions are 73/130,36/109,969/500

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 73/130,36/109,969/500, numerators are 73,36,969

Denominators are 130,109,500

The GCF of 73,36,969 is 1 .

LCM of 130,109,500 is 708500.

The greatest common factor of 73/130,36/109,969/500 = [GCF of 73,36,969]/[LCM of 130,109,500]= 1/708500

Therefore, the GCF of 73/130,36/109,969/500 is 1/708500.

Greatest Common Factor of 73,36,969

To find the highest common factor of 73,36,969, we have to find the factors of both numbers and list the highest common factor.

The factors of 73 are 1, 73

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

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The HCF of 73,36,969 is 1.

Lets's calculate GCF of 73,36,969

Greatest Common Factor (GCF) of 73,36,969 By Common Division

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

Greatest Common Factor of 73,36,969 By Matching Biggest Common Factor Method

Now, list down the factors of 73

1,73

Now, list down the factors of 36

1,2,3,4,6,9,12,18,36

Now, list down the factors of 969

1,3,17,19,51,57,323,969

Greatest Common Factor

We found the factors 73,36,969 . The biggest common factor number is the GCF number.
So the greatest common factor 73,36,969 is 1.

Lets's calculate LCM of 130,109,500

Lowest Common Multiple of 130,109,500 using Common Division

2	130, 109, 500
5	65, 109, 250
	13, 109, 50

∴ So the LCM of the given numbers is 2 x 5 x 13 x 109 x 50 = 708500

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/708500

Therefore, the GCF of Fractions 73/130,36/109,969/500 is 1/708500

Least Common Multiple of 130,109,500 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 130,109,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(130,109,500) = 1

common factors(in case of two or more numbers have common factors) = 10

GCF(130,109,500) x common factors =1 x 10 = 10

LCM(130,109,500) = ( 130 × 109 × 500 ) / 10

LCM(130,109,500) = 7085000 / 10

LCM(130,109,500) = 708500

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 73/130, 36/109, 969/500

1. What is the HCF of 73,36,969?

The HCF of 73,36,969 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 73/130, 36/109, 969/500?

Answer: GCF of Numerators as per given numbers 73/130, 36/109, 969/500 is

GCF of Numerators i.e. for 73,36,969 is 1

LCM of denominators i.e. for 130,109,500 is 708500.

Thus, GCF of Fractions is 1/708500.Finally, GCF of Fractions for 73/130, 36/109, 969/500 is 1/708500.