GCF of 998/204, 9690/838
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 998/204, 9690/838 i.e 2/85476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 998/204, 9690/838.
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 998/204,9690/838?
Given fractions are 998/204,9690/838
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 998/204,9690/838, numerators are 998,9690
Denominators are 204,838
The GCF of 998,9690 is 2 .
LCM of 204,838 is 85476.
The greatest common factor of 998/204,9690/838 = [GCF of 998,9690]/[LCM of 204,838]= 2/85476
Therefore, the GCF of 998/204,9690/838 is 2/85476.
To find the highest common factor of 998,9690, we have to find the factors of both numbers and list the highest common factor.
The factors of 998 are 1, 2, 499, 998
The factors of 9690 are 1, 2, 3, 5, 6, 10, 15, 17, 19, 30, 34, 38, 51, 57, 85, 95, 102, 114, 170, 190, 255, 285, 323, 510, 570, 646, 969, 1615, 1938, 3230, 4845, 9690
The HCF of 998,9690 is 2.
Lets's calculate GCF of 998,9690
| 2 | 998, 9690 |
| 499, 4845 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 998,9690 By Matching Biggest Common Factor Method
Now, list down the factors of 998
:1,2,499,998
Now, list down the factors of 9690
:1,2,3,5,6,10,15,17,19,30,34,38,51,57,85,95,102,114,170,190,255,285,323,510,570,646,969,1615,1938,3230,4845,9690
Greatest Common Factor
We found the factors 998,9690 . The biggest common factor number is the GCF number.
So the greatest common factor 998,9690 is 2.
Lets's calculate LCM of 204,838
| 2 | 204, 838 |
| 102, 419 |
∴ So the LCM of the given numbers is 2 x 102 x 419 = 85476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/85476
Therefore, the GCF of Fractions 998/204,9690/838 is 2/85476
Least Common Multiple of 204,838 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 204,838 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,838) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(204,838) x common factors =2 x 1 = 2
LCM(204,838) = ( 204 × 838 ) / 2
LCM(204,838) = 170952 / 2
LCM(204,838) = 85476
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FAQs on GCF of Fractions of 998/204, 9690/838
1. What is the HCF of 998,9690?
The HCF of 998,9690 is 2
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 998/204, 9690/838?
Answer: GCF of Numerators as per given numbers 998/204, 9690/838 is
GCF of Numerators i.e. for 998,9690 is 2
LCM of denominators i.e. for 204,838 is 85476.
Thus, GCF of Fractions is 2/85476.Finally, GCF of Fractions for 998/204, 9690/838 is 2/85476.