Use our free GCF of Fractions Calculator tool to compute the GCF of 783/115, 616/135 i.e 1/3105 easily. The following is the detailed procedure to determine the greatest common factor of fractions 783/115, 616/135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 783/115,616/135
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 783/115,616/135, numerators are 783,616
Denominators are 115,135
The GCF of 783,616 is 1 .
LCM of 115,135 is 3105.
The greatest common factor of 783/115,616/135 = [GCF of 783,616]/[LCM of 115,135]= 1/3105
Therefore, the GCF of 783/115,616/135 is 1/3105.
To find the highest common factor of 783,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 783,616 is 1.
Lets's calculate GCF of 783,616
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 783
:1,3,9,27,29,87,261,783
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 783,616 . The biggest common factor number is the GCF number.
So the greatest common factor 783,616 is 1.
Lets's calculate LCM of 115,135
5 | 115, 135 |
23, 27 |
∴ So the LCM of the given numbers is 5 x 23 x 27 = 3105
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3105
Therefore, the GCF of Fractions 783/115,616/135 is 1/3105
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 115,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(115,135) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(115,135) x common factors =5 x 1 = 5
LCM(115,135) = ( 115 × 135 ) / 5
LCM(115,135) = 15525 / 5
LCM(115,135) = 3105
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 783,616?
The HCF of 783,616 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 783/115, 616/135?
Answer: GCF of Numerators as per given numbers 783/115, 616/135 is
GCF of Numerators i.e. for 783,616 is 1
LCM of denominators i.e. for 115,135 is 3105.
Thus, GCF of Fractions is 1/3105.Finally, GCF of Fractions for 783/115, 616/135 is 1/3105.