GCF of 361/54, 209/2898
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 361/54, 209/2898 i.e 19/8694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 361/54, 209/2898.
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 361/54,209/2898?
Given fractions are 361/54,209/2898
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 361/54,209/2898, numerators are 361,209
Denominators are 54,2898
The GCF of 361,209 is 19 .
LCM of 54,2898 is 8694.
The greatest common factor of 361/54,209/2898 = [GCF of 361,209]/[LCM of 54,2898]= 19/8694
Therefore, the GCF of 361/54,209/2898 is 19/8694.
To find the highest common factor of 361,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 361 are 1, 19, 361
The factors of 209 are 1, 11, 19, 209
The HCF of 361,209 is 19.
Lets's calculate GCF of 361,209
| 19 | 361, 209 |
| 19, 11 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 361,209 By Matching Biggest Common Factor Method
Now, list down the factors of 361
:1,19,361
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 361,209 . The biggest common factor number is the GCF number.
So the greatest common factor 361,209 is 19.
Lets's calculate LCM of 54,2898
| 2 | 54, 2898 |
| 3 | 27, 1449 |
| 3 | 9, 483 |
| 3, 161 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 161 = 8694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/8694
Therefore, the GCF of Fractions 361/54,209/2898 is 19/8694
Least Common Multiple of 54,2898 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 54,2898 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,2898) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(54,2898) x common factors =18 x 1 = 18
LCM(54,2898) = ( 54 × 2898 ) / 18
LCM(54,2898) = 156492 / 18
LCM(54,2898) = 8694
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FAQs on GCF of Fractions of 361/54, 209/2898
1. What is the HCF of 361,209?
The HCF of 361,209 is 19
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 361/54, 209/2898?
Answer: GCF of Numerators as per given numbers 361/54, 209/2898 is
GCF of Numerators i.e. for 361,209 is 19
LCM of denominators i.e. for 54,2898 is 8694.
Thus, GCF of Fractions is 19/8694.Finally, GCF of Fractions for 361/54, 209/2898 is 19/8694.