GCF of 2198/322, 3309/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2198/322, 3309/728 i.e 1/16744 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2198/322, 3309/728.
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 2198/322,3309/728?
Given fractions are 2198/322,3309/728
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 2198/322,3309/728, numerators are 2198,3309
Denominators are 322,728
The GCF of 2198,3309 is 1 .
LCM of 322,728 is 16744.
The greatest common factor of 2198/322,3309/728 = [GCF of 2198,3309]/[LCM of 322,728]= 1/16744
Therefore, the GCF of 2198/322,3309/728 is 1/16744.
To find the highest common factor of 2198,3309, we have to find the factors of both numbers and list the highest common factor.
The factors of 2198 are 1, 2, 7, 14, 157, 314, 1099, 2198
The factors of 3309 are 1, 3, 1103, 3309
The HCF of 2198,3309 is 1.
Lets's calculate GCF of 2198,3309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2198,3309 By Matching Biggest Common Factor Method
Now, list down the factors of 2198
:1,2,7,14,157,314,1099,2198
Now, list down the factors of 3309
:1,3,1103,3309
Greatest Common Factor
We found the factors 2198,3309 . The biggest common factor number is the GCF number.
So the greatest common factor 2198,3309 is 1.
Lets's calculate LCM of 322,728
| 2 | 322, 728 |
| 7 | 161, 364 |
| 23, 52 |
∴ So the LCM of the given numbers is 2 x 7 x 23 x 52 = 16744
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16744
Therefore, the GCF of Fractions 2198/322,3309/728 is 1/16744
Least Common Multiple of 322,728 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 322,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(322,728) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(322,728) x common factors =14 x 1 = 14
LCM(322,728) = ( 322 × 728 ) / 14
LCM(322,728) = 234416 / 14
LCM(322,728) = 16744
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FAQs on GCF of Fractions of 2198/322, 3309/728
1. What is the HCF of 2198,3309?
The HCF of 2198,3309 is 1
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 2198/322, 3309/728?
Answer: GCF of Numerators as per given numbers 2198/322, 3309/728 is
GCF of Numerators i.e. for 2198,3309 is 1
LCM of denominators i.e. for 322,728 is 16744.
Thus, GCF of Fractions is 1/16744.Finally, GCF of Fractions for 2198/322, 3309/728 is 1/16744.