GCF of 9706/360, 9288/9600
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9706/360, 9288/9600 i.e 2/28800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9706/360, 9288/9600.
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 9706/360,9288/9600?
Given fractions are 9706/360,9288/9600
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 9706/360,9288/9600, numerators are 9706,9288
Denominators are 360,9600
The GCF of 9706,9288 is 2 .
LCM of 360,9600 is 28800.
The greatest common factor of 9706/360,9288/9600 = [GCF of 9706,9288]/[LCM of 360,9600]= 2/28800
Therefore, the GCF of 9706/360,9288/9600 is 2/28800.
To find the highest common factor of 9706,9288, we have to find the factors of both numbers and list the highest common factor.
The factors of 9706 are 1, 2, 23, 46, 211, 422, 4853, 9706
The factors of 9288 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 43, 54, 72, 86, 108, 129, 172, 216, 258, 344, 387, 516, 774, 1032, 1161, 1548, 2322, 3096, 4644, 9288
The HCF of 9706,9288 is 2.
Lets's calculate GCF of 9706,9288
| 2 | 9706, 9288 |
| 4853, 4644 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 9706,9288 By Matching Biggest Common Factor Method
Now, list down the factors of 9706
:1,2,23,46,211,422,4853,9706
Now, list down the factors of 9288
:1,2,3,4,6,8,9,12,18,24,27,36,43,54,72,86,108,129,172,216,258,344,387,516,774,1032,1161,1548,2322,3096,4644,9288
Greatest Common Factor
We found the factors 9706,9288 . The biggest common factor number is the GCF number.
So the greatest common factor 9706,9288 is 2.
Lets's calculate LCM of 360,9600
| 2 | 360, 9600 |
| 2 | 180, 4800 |
| 2 | 90, 2400 |
| 3 | 45, 1200 |
| 5 | 15, 400 |
| 3, 80 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 3 x 80 = 28800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/28800
Therefore, the GCF of Fractions 9706/360,9288/9600 is 2/28800
Least Common Multiple of 360,9600 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 360,9600 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,9600) = 120
common factors(in case of two or more numbers have common factors) = 1
GCF(360,9600) x common factors =120 x 1 = 120
LCM(360,9600) = ( 360 × 9600 ) / 120
LCM(360,9600) = 3456000 / 120
LCM(360,9600) = 28800
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FAQs on GCF of Fractions of 9706/360, 9288/9600
1. What is the HCF of 9706,9288?
The HCF of 9706,9288 is 2
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 9706/360, 9288/9600?
Answer: GCF of Numerators as per given numbers 9706/360, 9288/9600 is
GCF of Numerators i.e. for 9706,9288 is 2
LCM of denominators i.e. for 360,9600 is 28800.
Thus, GCF of Fractions is 2/28800.Finally, GCF of Fractions for 9706/360, 9288/9600 is 2/28800.