GCF of 3414/198, 5259/548
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3414/198, 5259/548 i.e 3/54252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3414/198, 5259/548.
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 3414/198,5259/548?
Given fractions are 3414/198,5259/548
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 3414/198,5259/548, numerators are 3414,5259
Denominators are 198,548
The GCF of 3414,5259 is 3 .
LCM of 198,548 is 54252.
The greatest common factor of 3414/198,5259/548 = [GCF of 3414,5259]/[LCM of 198,548]= 3/54252
Therefore, the GCF of 3414/198,5259/548 is 3/54252.
To find the highest common factor of 3414,5259, we have to find the factors of both numbers and list the highest common factor.
The factors of 3414 are 1, 2, 3, 6, 569, 1138, 1707, 3414
The factors of 5259 are 1, 3, 1753, 5259
The HCF of 3414,5259 is 3.
Lets's calculate GCF of 3414,5259
| 3 | 3414, 5259 |
| 1138, 1753 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3414,5259 By Matching Biggest Common Factor Method
Now, list down the factors of 3414
:1,2,3,6,569,1138,1707,3414
Now, list down the factors of 5259
:1,3,1753,5259
Greatest Common Factor
We found the factors 3414,5259 . The biggest common factor number is the GCF number.
So the greatest common factor 3414,5259 is 3.
Lets's calculate LCM of 198,548
| 2 | 198, 548 |
| 99, 274 |
∴ So the LCM of the given numbers is 2 x 99 x 274 = 54252
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/54252
Therefore, the GCF of Fractions 3414/198,5259/548 is 3/54252
Least Common Multiple of 198,548 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 198,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,548) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(198,548) x common factors =2 x 1 = 2
LCM(198,548) = ( 198 × 548 ) / 2
LCM(198,548) = 108504 / 2
LCM(198,548) = 54252
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FAQs on GCF of Fractions of 3414/198, 5259/548
1. What is the HCF of 3414,5259?
The HCF of 3414,5259 is 3
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 3414/198, 5259/548?
Answer: GCF of Numerators as per given numbers 3414/198, 5259/548 is
GCF of Numerators i.e. for 3414,5259 is 3
LCM of denominators i.e. for 198,548 is 54252.
Thus, GCF of Fractions is 3/54252.Finally, GCF of Fractions for 3414/198, 5259/548 is 3/54252.