GCF of 104/17, 384/6289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 104/17, 384/6289 i.e 8/106913 easily. The following is the detailed procedure to determine the greatest common factor of fractions 104/17, 384/6289.
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 104/17,384/6289?
Given fractions are 104/17,384/6289
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 104/17,384/6289, numerators are 104,384
Denominators are 17,6289
The GCF of 104,384 is 8 .
LCM of 17,6289 is 106913.
The greatest common factor of 104/17,384/6289 = [GCF of 104,384]/[LCM of 17,6289]= 8/106913
Therefore, the GCF of 104/17,384/6289 is 8/106913.
To find the highest common factor of 104,384, we have to find the factors of both numbers and list the highest common factor.
The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 104,384 is 8.
Lets's calculate GCF of 104,384
| 2 | 104, 384 |
| 2 | 52, 192 |
| 2 | 26, 96 |
| 13, 48 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 104,384 By Matching Biggest Common Factor Method
Now, list down the factors of 104
:1,2,4,8,13,26,52,104
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 104,384 . The biggest common factor number is the GCF number.
So the greatest common factor 104,384 is 8.
Lets's calculate LCM of 17,6289
Given numbers has no common factors except 1. So, there LCM is their product i.e 106913
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/106913
Therefore, the GCF of Fractions 104/17,384/6289 is 8/106913
Least Common Multiple of 17,6289 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 17,6289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,6289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,6289) x common factors =1 x 1 = 1
LCM(17,6289) = ( 17 × 6289 ) / 1
LCM(17,6289) = 106913 / 1
LCM(17,6289) = 106913
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FAQs on GCF of Fractions of 104/17, 384/6289
1. What is the HCF of 104,384?
The HCF of 104,384 is 8
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 104/17, 384/6289?
Answer: GCF of Numerators as per given numbers 104/17, 384/6289 is
GCF of Numerators i.e. for 104,384 is 8
LCM of denominators i.e. for 17,6289 is 106913.
Thus, GCF of Fractions is 8/106913.Finally, GCF of Fractions for 104/17, 384/6289 is 8/106913.