GCF of 5421/288, 4342/1916
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5421/288, 4342/1916 i.e 13/137952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5421/288, 4342/1916.
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 5421/288,4342/1916?
Given fractions are 5421/288,4342/1916
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 5421/288,4342/1916, numerators are 5421,4342
Denominators are 288,1916
The GCF of 5421,4342 is 13 .
LCM of 288,1916 is 137952.
The greatest common factor of 5421/288,4342/1916 = [GCF of 5421,4342]/[LCM of 288,1916]= 13/137952
Therefore, the GCF of 5421/288,4342/1916 is 13/137952.
To find the highest common factor of 5421,4342, we have to find the factors of both numbers and list the highest common factor.
The factors of 5421 are 1, 3, 13, 39, 139, 417, 1807, 5421
The factors of 4342 are 1, 2, 13, 26, 167, 334, 2171, 4342
The HCF of 5421,4342 is 13.
Lets's calculate GCF of 5421,4342
| 13 | 5421, 4342 |
| 417, 334 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 5421,4342 By Matching Biggest Common Factor Method
Now, list down the factors of 5421
:1,3,13,39,139,417,1807,5421
Now, list down the factors of 4342
:1,2,13,26,167,334,2171,4342
Greatest Common Factor
We found the factors 5421,4342 . The biggest common factor number is the GCF number.
So the greatest common factor 5421,4342 is 13.
Lets's calculate LCM of 288,1916
| 2 | 288, 1916 |
| 2 | 144, 958 |
| 72, 479 |
∴ So the LCM of the given numbers is 2 x 2 x 72 x 479 = 137952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/137952
Therefore, the GCF of Fractions 5421/288,4342/1916 is 13/137952
Least Common Multiple of 288,1916 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 288,1916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,1916) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(288,1916) x common factors =4 x 1 = 4
LCM(288,1916) = ( 288 × 1916 ) / 4
LCM(288,1916) = 551808 / 4
LCM(288,1916) = 137952
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FAQs on GCF of Fractions of 5421/288, 4342/1916
1. What is the HCF of 5421,4342?
The HCF of 5421,4342 is 13
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 5421/288, 4342/1916?
Answer: GCF of Numerators as per given numbers 5421/288, 4342/1916 is
GCF of Numerators i.e. for 5421,4342 is 13
LCM of denominators i.e. for 288,1916 is 137952.
Thus, GCF of Fractions is 13/137952.Finally, GCF of Fractions for 5421/288, 4342/1916 is 13/137952.