GCF of 6789/681, 4320/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6789/681, 4320/105 i.e 3/23835 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6789/681, 4320/105.
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 6789/681,4320/105?
Given fractions are 6789/681,4320/105
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 6789/681,4320/105, numerators are 6789,4320
Denominators are 681,105
The GCF of 6789,4320 is 3 .
LCM of 681,105 is 23835.
The greatest common factor of 6789/681,4320/105 = [GCF of 6789,4320]/[LCM of 681,105]= 3/23835
Therefore, the GCF of 6789/681,4320/105 is 3/23835.
To find the highest common factor of 6789,4320, we have to find the factors of both numbers and list the highest common factor.
The factors of 6789 are 1, 3, 31, 73, 93, 219, 2263, 6789
The factors of 4320 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, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160, 4320
The HCF of 6789,4320 is 3.
Lets's calculate GCF of 6789,4320
| 3 | 6789, 4320 |
| 2263, 1440 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 6789,4320 By Matching Biggest Common Factor Method
Now, list down the factors of 6789
:1,3,31,73,93,219,2263,6789
Now, list down the factors of 4320
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,32,36,40,45,48,54,60,72,80,90,96,108,120,135,144,160,180,216,240,270,288,360,432,480,540,720,864,1080,1440,2160,4320
Greatest Common Factor
We found the factors 6789,4320 . The biggest common factor number is the GCF number.
So the greatest common factor 6789,4320 is 3.
Lets's calculate LCM of 681,105
| 3 | 681, 105 |
| 227, 35 |
∴ So the LCM of the given numbers is 3 x 227 x 35 = 23835
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/23835
Therefore, the GCF of Fractions 6789/681,4320/105 is 3/23835
Least Common Multiple of 681,105 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 681,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(681,105) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(681,105) x common factors =3 x 1 = 3
LCM(681,105) = ( 681 × 105 ) / 3
LCM(681,105) = 71505 / 3
LCM(681,105) = 23835
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FAQs on GCF of Fractions of 6789/681, 4320/105
1. What is the HCF of 6789,4320?
The HCF of 6789,4320 is 3
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 6789/681, 4320/105?
Answer: GCF of Numerators as per given numbers 6789/681, 4320/105 is
GCF of Numerators i.e. for 6789,4320 is 3
LCM of denominators i.e. for 681,105 is 23835.
Thus, GCF of Fractions is 3/23835.Finally, GCF of Fractions for 6789/681, 4320/105 is 3/23835.