GCF of 8235/992, 9657/406
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8235/992, 9657/406 i.e 9/201376 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8235/992, 9657/406.
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 8235/992,9657/406?
Given fractions are 8235/992,9657/406
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 8235/992,9657/406, numerators are 8235,9657
Denominators are 992,406
The GCF of 8235,9657 is 9 .
LCM of 992,406 is 201376.
The greatest common factor of 8235/992,9657/406 = [GCF of 8235,9657]/[LCM of 992,406]= 9/201376
Therefore, the GCF of 8235/992,9657/406 is 9/201376.
To find the highest common factor of 8235,9657, we have to find the factors of both numbers and list the highest common factor.
The factors of 8235 are 1, 3, 5, 9, 15, 27, 45, 61, 135, 183, 305, 549, 915, 1647, 2745, 8235
The factors of 9657 are 1, 3, 9, 29, 37, 87, 111, 261, 333, 1073, 3219, 9657
The HCF of 8235,9657 is 9.
Lets's calculate GCF of 8235,9657
| 3 | 8235, 9657 |
| 3 | 2745, 3219 |
| 915, 1073 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 8235,9657 By Matching Biggest Common Factor Method
Now, list down the factors of 8235
:1,3,5,9,15,27,45,61,135,183,305,549,915,1647,2745,8235
Now, list down the factors of 9657
:1,3,9,29,37,87,111,261,333,1073,3219,9657
Greatest Common Factor
We found the factors 8235,9657 . The biggest common factor number is the GCF number.
So the greatest common factor 8235,9657 is 9.
Lets's calculate LCM of 992,406
| 2 | 992, 406 |
| 496, 203 |
∴ So the LCM of the given numbers is 2 x 496 x 203 = 201376
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/201376
Therefore, the GCF of Fractions 8235/992,9657/406 is 9/201376
Least Common Multiple of 992,406 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 992,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(992,406) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(992,406) x common factors =2 x 1 = 2
LCM(992,406) = ( 992 × 406 ) / 2
LCM(992,406) = 402752 / 2
LCM(992,406) = 201376
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FAQs on GCF of Fractions of 8235/992, 9657/406
1. What is the HCF of 8235,9657?
The HCF of 8235,9657 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 8235/992, 9657/406?
Answer: GCF of Numerators as per given numbers 8235/992, 9657/406 is
GCF of Numerators i.e. for 8235,9657 is 9
LCM of denominators i.e. for 992,406 is 201376.
Thus, GCF of Fractions is 9/201376.Finally, GCF of Fractions for 8235/992, 9657/406 is 9/201376.