GCF of 8204/838, 2194/7996
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8204/838, 2194/7996 i.e 2/3350324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8204/838, 2194/7996.
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 8204/838,2194/7996?
Given fractions are 8204/838,2194/7996
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 8204/838,2194/7996, numerators are 8204,2194
Denominators are 838,7996
The GCF of 8204,2194 is 2 .
LCM of 838,7996 is 3350324.
The greatest common factor of 8204/838,2194/7996 = [GCF of 8204,2194]/[LCM of 838,7996]= 2/3350324
Therefore, the GCF of 8204/838,2194/7996 is 2/3350324.
To find the highest common factor of 8204,2194, we have to find the factors of both numbers and list the highest common factor.
The factors of 8204 are 1, 2, 4, 7, 14, 28, 293, 586, 1172, 2051, 4102, 8204
The factors of 2194 are 1, 2, 1097, 2194
The HCF of 8204,2194 is 2.
Lets's calculate GCF of 8204,2194
| 2 | 8204, 2194 |
| 4102, 1097 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8204,2194 By Matching Biggest Common Factor Method
Now, list down the factors of 8204
:1,2,4,7,14,28,293,586,1172,2051,4102,8204
Now, list down the factors of 2194
:1,2,1097,2194
Greatest Common Factor
We found the factors 8204,2194 . The biggest common factor number is the GCF number.
So the greatest common factor 8204,2194 is 2.
Lets's calculate LCM of 838,7996
| 2 | 838, 7996 |
| 419, 3998 |
∴ So the LCM of the given numbers is 2 x 419 x 3998 = 3350324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3350324
Therefore, the GCF of Fractions 8204/838,2194/7996 is 2/3350324
Least Common Multiple of 838,7996 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 838,7996 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(838,7996) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(838,7996) x common factors =2 x 1 = 2
LCM(838,7996) = ( 838 × 7996 ) / 2
LCM(838,7996) = 6700648 / 2
LCM(838,7996) = 3350324
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FAQs on GCF of Fractions of 8204/838, 2194/7996
1. What is the HCF of 8204,2194?
The HCF of 8204,2194 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 8204/838, 2194/7996?
Answer: GCF of Numerators as per given numbers 8204/838, 2194/7996 is
GCF of Numerators i.e. for 8204,2194 is 2
LCM of denominators i.e. for 838,7996 is 3350324.
Thus, GCF of Fractions is 2/3350324.Finally, GCF of Fractions for 8204/838, 2194/7996 is 2/3350324.