How to Find GCF of 9729/970, 4697/4544?

GCF of 9729/970, 4697/4544

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 9729/970, 4697/4544 i.e 1/2203840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9729/970, 4697/4544.

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 9729/970,4697/4544?

Given fractions are 9729/970,4697/4544

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 9729/970,4697/4544, numerators are 9729,4697

Denominators are 970,4544

The GCF of 9729,4697 is 1 .

LCM of 970,4544 is 2203840.

The greatest common factor of 9729/970,4697/4544 = [GCF of 9729,4697]/[LCM of 970,4544]= 1/2203840

Therefore, the GCF of 9729/970,4697/4544 is 1/2203840.

Greatest Common Factor of 9729,4697

To find the highest common factor of 9729,4697, we have to find the factors of both numbers and list the highest common factor.

The factors of 9729 are 1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729

The factors of 4697 are 1, 7, 11, 61, 77, 427, 671, 4697

The HCF of 9729,4697 is 1.

Lets's calculate GCF of 9729,4697

Greatest Common Factor (GCF) of 9729,4697 By Common Division

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

Greatest Common Factor of 9729,4697 By Matching Biggest Common Factor Method

Now, list down the factors of 9729

1,3,9,23,47,69,141,207,423,1081,3243,9729

Now, list down the factors of 4697

1,7,11,61,77,427,671,4697

Greatest Common Factor

We found the factors 9729,4697 . The biggest common factor number is the GCF number.
So the greatest common factor 9729,4697 is 1.

Lets's calculate LCM of 970,4544

Lowest Common Multiple of 970,4544 using Common Division

2	970, 4544
	485, 2272

∴ So the LCM of the given numbers is 2 x 485 x 2272 = 2203840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2203840

Therefore, the GCF of Fractions 9729/970,4697/4544 is 1/2203840

Least Common Multiple of 970,4544 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 970,4544 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(970,4544) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(970,4544) x common factors =2 x 1 = 2

LCM(970,4544) = ( 970 × 4544 ) / 2

LCM(970,4544) = 4407680 / 2

LCM(970,4544) = 2203840

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 9729/970, 4697/4544

1. What is the HCF of 9729,4697?

The HCF of 9729,4697 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 9729/970, 4697/4544?

Answer: GCF of Numerators as per given numbers 9729/970, 4697/4544 is

GCF of Numerators i.e. for 9729,4697 is 1

LCM of denominators i.e. for 970,4544 is 2203840.

Thus, GCF of Fractions is 1/2203840.Finally, GCF of Fractions for 9729/970, 4697/4544 is 1/2203840.