Use our free GCF of Fractions Calculator tool to compute the GCF of 315/416, 965/922 i.e 5/191776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/416, 965/922.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 315/416,965/922
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 315/416,965/922, numerators are 315,965
Denominators are 416,922
The GCF of 315,965 is 5 .
LCM of 416,922 is 191776.
The greatest common factor of 315/416,965/922 = [GCF of 315,965]/[LCM of 416,922]= 5/191776
Therefore, the GCF of 315/416,965/922 is 5/191776.
To find the highest common factor of 315,965, we have to find the factors of both numbers and list the highest common factor.
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The factors of 965 are 1, 5, 193, 965
The HCF of 315,965 is 5.
Lets's calculate GCF of 315,965
5 | 315, 965 |
63, 193 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Now, list down the factors of 965
:1,5,193,965
Greatest Common Factor
We found the factors 315,965 . The biggest common factor number is the GCF number.
So the greatest common factor 315,965 is 5.
Lets's calculate LCM of 416,922
2 | 416, 922 |
208, 461 |
∴ So the LCM of the given numbers is 2 x 208 x 461 = 191776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/191776
Therefore, the GCF of Fractions 315/416,965/922 is 5/191776
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 416,922 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,922) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(416,922) x common factors =2 x 1 = 2
LCM(416,922) = ( 416 × 922 ) / 2
LCM(416,922) = 383552 / 2
LCM(416,922) = 191776
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 315,965?
The HCF of 315,965 is 5
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 315/416, 965/922?
Answer: GCF of Numerators as per given numbers 315/416, 965/922 is
GCF of Numerators i.e. for 315,965 is 5
LCM of denominators i.e. for 416,922 is 191776.
Thus, GCF of Fractions is 5/191776.Finally, GCF of Fractions for 315/416, 965/922 is 5/191776.