GCF of 9675/279, 8640/7164
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9675/279, 8640/7164 i.e 45/222084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9675/279, 8640/7164.
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 9675/279,8640/7164?
Given fractions are 9675/279,8640/7164
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 9675/279,8640/7164, numerators are 9675,8640
Denominators are 279,7164
The GCF of 9675,8640 is 45 .
LCM of 279,7164 is 222084.
The greatest common factor of 9675/279,8640/7164 = [GCF of 9675,8640]/[LCM of 279,7164]= 45/222084
Therefore, the GCF of 9675/279,8640/7164 is 45/222084.
To find the highest common factor of 9675,8640, we have to find the factors of both numbers and list the highest common factor.
The factors of 9675 are 1, 3, 5, 9, 15, 25, 43, 45, 75, 129, 215, 225, 387, 645, 1075, 1935, 3225, 9675
The factors of 8640 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 192, 216, 240, 270, 288, 320, 360, 432, 480, 540, 576, 720, 864, 960, 1080, 1440, 1728, 2160, 2880, 4320, 8640
The HCF of 9675,8640 is 45.
Lets's calculate GCF of 9675,8640
| 3 | 9675, 8640 |
| 3 | 3225, 2880 |
| 5 | 1075, 960 |
| 215, 192 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 9675,8640 By Matching Biggest Common Factor Method
Now, list down the factors of 9675
:1,3,5,9,15,25,43,45,75,129,215,225,387,645,1075,1935,3225,9675
Now, list down the factors of 8640
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,32,36,40,45,48,54,60,64,72,80,90,96,108,120,135,144,160,180,192,216,240,270,288,320,360,432,480,540,576,720,864,960,1080,1440,1728,2160,2880,4320,8640
Greatest Common Factor
We found the factors 9675,8640 . The biggest common factor number is the GCF number.
So the greatest common factor 9675,8640 is 45.
Lets's calculate LCM of 279,7164
| 3 | 279, 7164 |
| 3 | 93, 2388 |
| 31, 796 |
∴ So the LCM of the given numbers is 3 x 3 x 31 x 796 = 222084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/222084
Therefore, the GCF of Fractions 9675/279,8640/7164 is 45/222084
Least Common Multiple of 279,7164 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 279,7164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(279,7164) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(279,7164) x common factors =9 x 1 = 9
LCM(279,7164) = ( 279 × 7164 ) / 9
LCM(279,7164) = 1998756 / 9
LCM(279,7164) = 222084
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FAQs on GCF of Fractions of 9675/279, 8640/7164
1. What is the HCF of 9675,8640?
The HCF of 9675,8640 is 45
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 9675/279, 8640/7164?
Answer: GCF of Numerators as per given numbers 9675/279, 8640/7164 is
GCF of Numerators i.e. for 9675,8640 is 45
LCM of denominators i.e. for 279,7164 is 222084.
Thus, GCF of Fractions is 45/222084.Finally, GCF of Fractions for 9675/279, 8640/7164 is 45/222084.