GCF of 514/74, 198/323
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 514/74, 198/323 i.e 2/23902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/74, 198/323.
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 514/74,198/323?
Given fractions are 514/74,198/323
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 514/74,198/323, numerators are 514,198
Denominators are 74,323
The GCF of 514,198 is 2 .
LCM of 74,323 is 23902.
The greatest common factor of 514/74,198/323 = [GCF of 514,198]/[LCM of 74,323]= 2/23902
Therefore, the GCF of 514/74,198/323 is 2/23902.
To find the highest common factor of 514,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 514,198 is 2.
Lets's calculate GCF of 514,198
| 2 | 514, 198 |
| 257, 99 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 514,198 By Matching Biggest Common Factor Method
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 514,198 . The biggest common factor number is the GCF number.
So the greatest common factor 514,198 is 2.
Lets's calculate LCM of 74,323
Given numbers has no common factors except 1. So, there LCM is their product i.e 23902
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/23902
Therefore, the GCF of Fractions 514/74,198/323 is 2/23902
Least Common Multiple of 74,323 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 74,323 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,323) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(74,323) x common factors =1 x 1 = 1
LCM(74,323) = ( 74 × 323 ) / 1
LCM(74,323) = 23902 / 1
LCM(74,323) = 23902
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FAQs on GCF of Fractions of 514/74, 198/323
1. What is the HCF of 514,198?
The HCF of 514,198 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 514/74, 198/323?
Answer: GCF of Numerators as per given numbers 514/74, 198/323 is
GCF of Numerators i.e. for 514,198 is 2
LCM of denominators i.e. for 74,323 is 23902.
Thus, GCF of Fractions is 2/23902.Finally, GCF of Fractions for 514/74, 198/323 is 2/23902.