GCF of 8982/415, 9729/3985
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8982/415, 9729/3985 i.e 9/330755 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8982/415, 9729/3985.
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 8982/415,9729/3985?
Given fractions are 8982/415,9729/3985
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 8982/415,9729/3985, numerators are 8982,9729
Denominators are 415,3985
The GCF of 8982,9729 is 9 .
LCM of 415,3985 is 330755.
The greatest common factor of 8982/415,9729/3985 = [GCF of 8982,9729]/[LCM of 415,3985]= 9/330755
Therefore, the GCF of 8982/415,9729/3985 is 9/330755.
To find the highest common factor of 8982,9729, we have to find the factors of both numbers and list the highest common factor.
The factors of 8982 are 1, 2, 3, 6, 9, 18, 499, 998, 1497, 2994, 4491, 8982
The factors of 9729 are 1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729
The HCF of 8982,9729 is 9.
Lets's calculate GCF of 8982,9729
| 3 | 8982, 9729 |
| 3 | 2994, 3243 |
| 998, 1081 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 8982,9729 By Matching Biggest Common Factor Method
Now, list down the factors of 8982
:1,2,3,6,9,18,499,998,1497,2994,4491,8982
Now, list down the factors of 9729
:1,3,9,23,47,69,141,207,423,1081,3243,9729
Greatest Common Factor
We found the factors 8982,9729 . The biggest common factor number is the GCF number.
So the greatest common factor 8982,9729 is 9.
Lets's calculate LCM of 415,3985
| 5 | 415, 3985 |
| 83, 797 |
∴ So the LCM of the given numbers is 5 x 83 x 797 = 330755
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/330755
Therefore, the GCF of Fractions 8982/415,9729/3985 is 9/330755
Least Common Multiple of 415,3985 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 415,3985 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(415,3985) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(415,3985) x common factors =5 x 1 = 5
LCM(415,3985) = ( 415 × 3985 ) / 5
LCM(415,3985) = 1653775 / 5
LCM(415,3985) = 330755
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FAQs on GCF of Fractions of 8982/415, 9729/3985
1. What is the HCF of 8982,9729?
The HCF of 8982,9729 is 9
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 8982/415, 9729/3985?
Answer: GCF of Numerators as per given numbers 8982/415, 9729/3985 is
GCF of Numerators i.e. for 8982,9729 is 9
LCM of denominators i.e. for 415,3985 is 330755.
Thus, GCF of Fractions is 9/330755.Finally, GCF of Fractions for 8982/415, 9729/3985 is 9/330755.