GCF of 205/216, 398/378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 205/216, 398/378 i.e 1/1512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/216, 398/378.
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 205/216,398/378?
Given fractions are 205/216,398/378
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 205/216,398/378, numerators are 205,398
Denominators are 216,378
The GCF of 205,398 is 1 .
LCM of 216,378 is 1512.
The greatest common factor of 205/216,398/378 = [GCF of 205,398]/[LCM of 216,378]= 1/1512
Therefore, the GCF of 205/216,398/378 is 1/1512.
To find the highest common factor of 205,398, we have to find the factors of both numbers and list the highest common factor.
The factors of 205 are 1, 5, 41, 205
The factors of 398 are 1, 2, 199, 398
The HCF of 205,398 is 1.
Lets's calculate GCF of 205,398
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 205,398 By Matching Biggest Common Factor Method
Now, list down the factors of 205
:1,5,41,205
Now, list down the factors of 398
:1,2,199,398
Greatest Common Factor
We found the factors 205,398 . The biggest common factor number is the GCF number.
So the greatest common factor 205,398 is 1.
Lets's calculate LCM of 216,378
| 2 | 216, 378 |
| 3 | 108, 189 |
| 3 | 36, 63 |
| 3 | 12, 21 |
| 4, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 4 x 7 = 1512
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1512
Therefore, the GCF of Fractions 205/216,398/378 is 1/1512
Least Common Multiple of 216,378 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 216,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(216,378) = 54
common factors(in case of two or more numbers have common factors) = 1
GCF(216,378) x common factors =54 x 1 = 54
LCM(216,378) = ( 216 × 378 ) / 54
LCM(216,378) = 81648 / 54
LCM(216,378) = 1512
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 205/216, 398/378
1. What is the HCF of 205,398?
The HCF of 205,398 is 1
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 205/216, 398/378?
Answer: GCF of Numerators as per given numbers 205/216, 398/378 is
GCF of Numerators i.e. for 205,398 is 1
LCM of denominators i.e. for 216,378 is 1512.
Thus, GCF of Fractions is 1/1512.Finally, GCF of Fractions for 205/216, 398/378 is 1/1512.