GCF of 817/198, 418/963
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 817/198, 418/963 i.e 19/21186 easily. The following is the detailed procedure to determine the greatest common factor of fractions 817/198, 418/963.
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 817/198,418/963?
Given fractions are 817/198,418/963
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 817/198,418/963, numerators are 817,418
Denominators are 198,963
The GCF of 817,418 is 19 .
LCM of 198,963 is 21186.
The greatest common factor of 817/198,418/963 = [GCF of 817,418]/[LCM of 198,963]= 19/21186
Therefore, the GCF of 817/198,418/963 is 19/21186.
To find the highest common factor of 817,418, we have to find the factors of both numbers and list the highest common factor.
The factors of 817 are 1, 19, 43, 817
The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418
The HCF of 817,418 is 19.
Lets's calculate GCF of 817,418
| 19 | 817, 418 |
| 43, 22 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 817,418 By Matching Biggest Common Factor Method
Now, list down the factors of 817
:1,19,43,817
Now, list down the factors of 418
:1,2,11,19,22,38,209,418
Greatest Common Factor
We found the factors 817,418 . The biggest common factor number is the GCF number.
So the greatest common factor 817,418 is 19.
Lets's calculate LCM of 198,963
| 3 | 198, 963 |
| 3 | 66, 321 |
| 22, 107 |
∴ So the LCM of the given numbers is 3 x 3 x 22 x 107 = 21186
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/21186
Therefore, the GCF of Fractions 817/198,418/963 is 19/21186
Least Common Multiple of 198,963 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 198,963 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,963) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(198,963) x common factors =9 x 1 = 9
LCM(198,963) = ( 198 × 963 ) / 9
LCM(198,963) = 190674 / 9
LCM(198,963) = 21186
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FAQs on GCF of Fractions of 817/198, 418/963
1. What is the HCF of 817,418?
The HCF of 817,418 is 19
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 817/198, 418/963?
Answer: GCF of Numerators as per given numbers 817/198, 418/963 is
GCF of Numerators i.e. for 817,418 is 19
LCM of denominators i.e. for 198,963 is 21186.
Thus, GCF of Fractions is 19/21186.Finally, GCF of Fractions for 817/198, 418/963 is 19/21186.