GCF of 8640/851, 8224/6784
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8640/851, 8224/6784 i.e 32/5773184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8640/851, 8224/6784.
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 8640/851,8224/6784?
Given fractions are 8640/851,8224/6784
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 8640/851,8224/6784, numerators are 8640,8224
Denominators are 851,6784
The GCF of 8640,8224 is 32 .
LCM of 851,6784 is 5773184.
The greatest common factor of 8640/851,8224/6784 = [GCF of 8640,8224]/[LCM of 851,6784]= 32/5773184
Therefore, the GCF of 8640/851,8224/6784 is 32/5773184.
To find the highest common factor of 8640,8224, 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 8224 are 1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112, 8224
The HCF of 8640,8224 is 32.
Lets's calculate GCF of 8640,8224
| 2 | 8640, 8224 |
| 2 | 4320, 4112 |
| 2 | 2160, 2056 |
| 2 | 1080, 1028 |
| 2 | 540, 514 |
| 270, 257 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 8640,8224 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 8224
:1,2,4,8,16,32,257,514,1028,2056,4112,8224
Greatest Common Factor
We found the factors 8640,8224 . The biggest common factor number is the GCF number.
So the greatest common factor 8640,8224 is 32.
Lets's calculate LCM of 851,6784
Given numbers has no common factors except 1. So, there LCM is their product i.e 5773184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/5773184
Therefore, the GCF of Fractions 8640/851,8224/6784 is 32/5773184
Least Common Multiple of 851,6784 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 851,6784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(851,6784) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(851,6784) x common factors =1 x 1 = 1
LCM(851,6784) = ( 851 × 6784 ) / 1
LCM(851,6784) = 5773184 / 1
LCM(851,6784) = 5773184
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FAQs on GCF of Fractions of 8640/851, 8224/6784
1. What is the HCF of 8640,8224?
The HCF of 8640,8224 is 32
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 8640/851, 8224/6784?
Answer: GCF of Numerators as per given numbers 8640/851, 8224/6784 is
GCF of Numerators i.e. for 8640,8224 is 32
LCM of denominators i.e. for 851,6784 is 5773184.
Thus, GCF of Fractions is 32/5773184.Finally, GCF of Fractions for 8640/851, 8224/6784 is 32/5773184.