GCF of 8640/315, 1386/190
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8640/315, 1386/190 i.e 18/11970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8640/315, 1386/190.
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 8640/315,1386/190?
Given fractions are 8640/315,1386/190
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 8640/315,1386/190, numerators are 8640,1386
Denominators are 315,190
The GCF of 8640,1386 is 18 .
LCM of 315,190 is 11970.
The greatest common factor of 8640/315,1386/190 = [GCF of 8640,1386]/[LCM of 315,190]= 18/11970
Therefore, the GCF of 8640/315,1386/190 is 18/11970.
To find the highest common factor of 8640,1386, we have to find the factors of both numbers and list the highest common factor.
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 factors of 1386 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 63, 66, 77, 99, 126, 154, 198, 231, 462, 693, 1386
The HCF of 8640,1386 is 18.
Lets's calculate GCF of 8640,1386
| 2 | 8640, 1386 |
| 3 | 4320, 693 |
| 3 | 1440, 231 |
| 480, 77 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 8640,1386 By Matching Biggest Common Factor Method
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
Now, list down the factors of 1386
:1,2,3,6,7,9,11,14,18,21,22,33,42,63,66,77,99,126,154,198,231,462,693,1386
Greatest Common Factor
We found the factors 8640,1386 . The biggest common factor number is the GCF number.
So the greatest common factor 8640,1386 is 18.
Lets's calculate LCM of 315,190
| 5 | 315, 190 |
| 63, 38 |
∴ So the LCM of the given numbers is 5 x 63 x 38 = 11970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/11970
Therefore, the GCF of Fractions 8640/315,1386/190 is 18/11970
Least Common Multiple of 315,190 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 315,190 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(315,190) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(315,190) x common factors =5 x 1 = 5
LCM(315,190) = ( 315 × 190 ) / 5
LCM(315,190) = 59850 / 5
LCM(315,190) = 11970
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FAQs on GCF of Fractions of 8640/315, 1386/190
1. What is the HCF of 8640,1386?
The HCF of 8640,1386 is 18
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 8640/315, 1386/190?
Answer: GCF of Numerators as per given numbers 8640/315, 1386/190 is
GCF of Numerators i.e. for 8640,1386 is 18
LCM of denominators i.e. for 315,190 is 11970.
Thus, GCF of Fractions is 18/11970.Finally, GCF of Fractions for 8640/315, 1386/190 is 18/11970.