GCF of 9600/438, 7830/9054
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9600/438, 7830/9054 i.e 30/660942 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9600/438, 7830/9054.
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 9600/438,7830/9054?
Given fractions are 9600/438,7830/9054
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 9600/438,7830/9054, numerators are 9600,7830
Denominators are 438,9054
The GCF of 9600,7830 is 30 .
LCM of 438,9054 is 660942.
The greatest common factor of 9600/438,7830/9054 = [GCF of 9600,7830]/[LCM of 438,9054]= 30/660942
Therefore, the GCF of 9600/438,7830/9054 is 30/660942.
To find the highest common factor of 9600,7830, we have to find the factors of both numbers and list the highest common factor.
The factors of 9600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600
The factors of 7830 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830
The HCF of 9600,7830 is 30.
Lets's calculate GCF of 9600,7830
| 2 | 9600, 7830 |
| 3 | 4800, 3915 |
| 5 | 1600, 1305 |
| 320, 261 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 9600,7830 By Matching Biggest Common Factor Method
Now, list down the factors of 9600
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,32,40,48,50,60,64,75,80,96,100,120,128,150,160,192,200,240,300,320,384,400,480,600,640,800,960,1200,1600,1920,2400,3200,4800,9600
Now, list down the factors of 7830
:1,2,3,5,6,9,10,15,18,27,29,30,45,54,58,87,90,135,145,174,261,270,290,435,522,783,870,1305,1566,2610,3915,7830
Greatest Common Factor
We found the factors 9600,7830 . The biggest common factor number is the GCF number.
So the greatest common factor 9600,7830 is 30.
Lets's calculate LCM of 438,9054
| 2 | 438, 9054 |
| 3 | 219, 4527 |
| 73, 1509 |
∴ So the LCM of the given numbers is 2 x 3 x 73 x 1509 = 660942
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/660942
Therefore, the GCF of Fractions 9600/438,7830/9054 is 30/660942
Least Common Multiple of 438,9054 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 438,9054 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(438,9054) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(438,9054) x common factors =6 x 1 = 6
LCM(438,9054) = ( 438 × 9054 ) / 6
LCM(438,9054) = 3965652 / 6
LCM(438,9054) = 660942
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FAQs on GCF of Fractions of 9600/438, 7830/9054
1. What is the HCF of 9600,7830?
The HCF of 9600,7830 is 30
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 9600/438, 7830/9054?
Answer: GCF of Numerators as per given numbers 9600/438, 7830/9054 is
GCF of Numerators i.e. for 9600,7830 is 30
LCM of denominators i.e. for 438,9054 is 660942.
Thus, GCF of Fractions is 30/660942.Finally, GCF of Fractions for 9600/438, 7830/9054 is 30/660942.