Use our free GCF of Fractions Calculator tool to compute the GCF of 216/616, 864/313 i.e 216/192808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/616, 864/313.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 216/616,864/313
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 216/616,864/313, numerators are 216,864
Denominators are 616,313
The GCF of 216,864 is 216 .
LCM of 616,313 is 192808.
The greatest common factor of 216/616,864/313 = [GCF of 216,864]/[LCM of 616,313]= 216/192808
Therefore, the GCF of 216/616,864/313 is 216/192808.
To find the highest common factor of 216,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 216,864 is 216.
Lets's calculate GCF of 216,864
2 | 216, 864 |
2 | 108, 432 |
2 | 54, 216 |
3 | 27, 108 |
3 | 9, 36 |
3 | 3, 12 |
1, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 3 x 3 = 216
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 216,864 . The biggest common factor number is the GCF number.
So the greatest common factor 216,864 is 216.
Lets's calculate LCM of 616,313
Given numbers has no common factors except 1. So, there LCM is their product i.e 192808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 216/192808
Therefore, the GCF of Fractions 216/616,864/313 is 216/192808
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 616,313 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(616,313) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(616,313) x common factors =1 x 1 = 1
LCM(616,313) = ( 616 × 313 ) / 1
LCM(616,313) = 192808 / 1
LCM(616,313) = 192808
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 216,864?
The HCF of 216,864 is 216
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 216/616, 864/313?
Answer: GCF of Numerators as per given numbers 216/616, 864/313 is
GCF of Numerators i.e. for 216,864 is 216
LCM of denominators i.e. for 616,313 is 192808.
Thus, GCF of Fractions is 216/192808.Finally, GCF of Fractions for 216/616, 864/313 is 216/192808.