GCF of 2398/343, 5414/5537
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2398/343, 5414/5537 i.e 2/38759 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2398/343, 5414/5537.
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 2398/343,5414/5537?
Given fractions are 2398/343,5414/5537
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 2398/343,5414/5537, numerators are 2398,5414
Denominators are 343,5537
The GCF of 2398,5414 is 2 .
LCM of 343,5537 is 38759.
The greatest common factor of 2398/343,5414/5537 = [GCF of 2398,5414]/[LCM of 343,5537]= 2/38759
Therefore, the GCF of 2398/343,5414/5537 is 2/38759.
To find the highest common factor of 2398,5414, we have to find the factors of both numbers and list the highest common factor.
The factors of 2398 are 1, 2, 11, 22, 109, 218, 1199, 2398
The factors of 5414 are 1, 2, 2707, 5414
The HCF of 2398,5414 is 2.
Lets's calculate GCF of 2398,5414
| 2 | 2398, 5414 |
| 1199, 2707 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2398,5414 By Matching Biggest Common Factor Method
Now, list down the factors of 2398
:1,2,11,22,109,218,1199,2398
Now, list down the factors of 5414
:1,2,2707,5414
Greatest Common Factor
We found the factors 2398,5414 . The biggest common factor number is the GCF number.
So the greatest common factor 2398,5414 is 2.
Lets's calculate LCM of 343,5537
| 7 | 343, 5537 |
| 7 | 49, 791 |
| 7, 113 |
∴ So the LCM of the given numbers is 7 x 7 x 7 x 113 = 38759
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38759
Therefore, the GCF of Fractions 2398/343,5414/5537 is 2/38759
Least Common Multiple of 343,5537 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 343,5537 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,5537) = 49
common factors(in case of two or more numbers have common factors) = 1
GCF(343,5537) x common factors =49 x 1 = 49
LCM(343,5537) = ( 343 × 5537 ) / 49
LCM(343,5537) = 1899191 / 49
LCM(343,5537) = 38759
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FAQs on GCF of Fractions of 2398/343, 5414/5537
1. What is the HCF of 2398,5414?
The HCF of 2398,5414 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 2398/343, 5414/5537?
Answer: GCF of Numerators as per given numbers 2398/343, 5414/5537 is
GCF of Numerators i.e. for 2398,5414 is 2
LCM of denominators i.e. for 343,5537 is 38759.
Thus, GCF of Fractions is 2/38759.Finally, GCF of Fractions for 2398/343, 5414/5537 is 2/38759.