GCF of 9729/963, 6180/3642
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9729/963, 6180/3642 i.e 3/1169082 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9729/963, 6180/3642.
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 9729/963,6180/3642?
Given fractions are 9729/963,6180/3642
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 9729/963,6180/3642, numerators are 9729,6180
Denominators are 963,3642
The GCF of 9729,6180 is 3 .
LCM of 963,3642 is 1169082.
The greatest common factor of 9729/963,6180/3642 = [GCF of 9729,6180]/[LCM of 963,3642]= 3/1169082
Therefore, the GCF of 9729/963,6180/3642 is 3/1169082.
To find the highest common factor of 9729,6180, 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 6180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180
The HCF of 9729,6180 is 3.
Lets's calculate GCF of 9729,6180
| 3 | 9729, 6180 |
| 3243, 2060 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9729,6180 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 6180
:1,2,3,4,5,6,10,12,15,20,30,60,103,206,309,412,515,618,1030,1236,1545,2060,3090,6180
Greatest Common Factor
We found the factors 9729,6180 . The biggest common factor number is the GCF number.
So the greatest common factor 9729,6180 is 3.
Lets's calculate LCM of 963,3642
| 3 | 963, 3642 |
| 321, 1214 |
∴ So the LCM of the given numbers is 3 x 321 x 1214 = 1169082
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1169082
Therefore, the GCF of Fractions 9729/963,6180/3642 is 3/1169082
Least Common Multiple of 963,3642 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 963,3642 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(963,3642) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(963,3642) x common factors =3 x 1 = 3
LCM(963,3642) = ( 963 × 3642 ) / 3
LCM(963,3642) = 3507246 / 3
LCM(963,3642) = 1169082
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FAQs on GCF of Fractions of 9729/963, 6180/3642
1. What is the HCF of 9729,6180?
The HCF of 9729,6180 is 3
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 9729/963, 6180/3642?
Answer: GCF of Numerators as per given numbers 9729/963, 6180/3642 is
GCF of Numerators i.e. for 9729,6180 is 3
LCM of denominators i.e. for 963,3642 is 1169082.
Thus, GCF of Fractions is 3/1169082.Finally, GCF of Fractions for 9729/963, 6180/3642 is 3/1169082.