Use our free GCF of Fractions Calculator tool to compute the GCF of 315/792, 312/360 i.e 3/3960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/792, 312/360.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 315/792,312/360
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 315/792,312/360, numerators are 315,312
Denominators are 792,360
The GCF of 315,312 is 3 .
LCM of 792,360 is 3960.
The greatest common factor of 315/792,312/360 = [GCF of 315,312]/[LCM of 792,360]= 3/3960
Therefore, the GCF of 315/792,312/360 is 3/3960.
To find the highest common factor of 315,312, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 315,312 is 3.
Lets's calculate GCF of 315,312
3 | 315, 312 |
105, 104 |
∴ So the GCF of the given numbers is 3 = 3
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 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 315,312 . The biggest common factor number is the GCF number.
So the greatest common factor 315,312 is 3.
Lets's calculate LCM of 792,360
2 | 792, 360 |
2 | 396, 180 |
2 | 198, 90 |
3 | 99, 45 |
3 | 33, 15 |
11, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 11 x 5 = 3960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3960
Therefore, the GCF of Fractions 315/792,312/360 is 3/3960
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 792,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(792,360) = 72
common factors(in case of two or more numbers have common factors) = 1
GCF(792,360) x common factors =72 x 1 = 72
LCM(792,360) = ( 792 × 360 ) / 72
LCM(792,360) = 285120 / 72
LCM(792,360) = 3960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 315,312?
The HCF of 315,312 is 3
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 315/792, 312/360?
Answer: GCF of Numerators as per given numbers 315/792, 312/360 is
GCF of Numerators i.e. for 315,312 is 3
LCM of denominators i.e. for 792,360 is 3960.
Thus, GCF of Fractions is 3/3960.Finally, GCF of Fractions for 315/792, 312/360 is 3/3960.