GCF of 9728/546, 8640/6780
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9728/546, 8640/6780 i.e 64/616980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9728/546, 8640/6780.
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 9728/546,8640/6780?
Given fractions are 9728/546,8640/6780
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 9728/546,8640/6780, numerators are 9728,8640
Denominators are 546,6780
The GCF of 9728,8640 is 64 .
LCM of 546,6780 is 616980.
The greatest common factor of 9728/546,8640/6780 = [GCF of 9728,8640]/[LCM of 546,6780]= 64/616980
Therefore, the GCF of 9728/546,8640/6780 is 64/616980.
To find the highest common factor of 9728,8640, we have to find the factors of both numbers and list the highest common factor.
The factors of 9728 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728
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 9728,8640 is 64.
Lets's calculate GCF of 9728,8640
| 2 | 9728, 8640 |
| 2 | 4864, 4320 |
| 2 | 2432, 2160 |
| 2 | 1216, 1080 |
| 2 | 608, 540 |
| 2 | 304, 270 |
| 152, 135 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64
Greatest Common Factor of 9728,8640 By Matching Biggest Common Factor Method
Now, list down the factors of 9728
:1,2,4,8,16,19,32,38,64,76,128,152,256,304,512,608,1216,2432,4864,9728
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 9728,8640 . The biggest common factor number is the GCF number.
So the greatest common factor 9728,8640 is 64.
Lets's calculate LCM of 546,6780
| 2 | 546, 6780 |
| 3 | 273, 3390 |
| 91, 1130 |
∴ So the LCM of the given numbers is 2 x 3 x 91 x 1130 = 616980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/616980
Therefore, the GCF of Fractions 9728/546,8640/6780 is 64/616980
Least Common Multiple of 546,6780 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 546,6780 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,6780) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(546,6780) x common factors =6 x 1 = 6
LCM(546,6780) = ( 546 × 6780 ) / 6
LCM(546,6780) = 3701880 / 6
LCM(546,6780) = 616980
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FAQs on GCF of Fractions of 9728/546, 8640/6780
1. What is the HCF of 9728,8640?
The HCF of 9728,8640 is 64
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 9728/546, 8640/6780?
Answer: GCF of Numerators as per given numbers 9728/546, 8640/6780 is
GCF of Numerators i.e. for 9728,8640 is 64
LCM of denominators i.e. for 546,6780 is 616980.
Thus, GCF of Fractions is 64/616980.Finally, GCF of Fractions for 9728/546, 8640/6780 is 64/616980.