Use our free GCF of Fractions Calculator tool to compute the GCF of 412/125, 120/315 i.e 4/7875 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/125, 120/315.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 412/125,120/315
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 412/125,120/315, numerators are 412,120
Denominators are 125,315
The GCF of 412,120 is 4 .
LCM of 125,315 is 7875.
The greatest common factor of 412/125,120/315 = [GCF of 412,120]/[LCM of 125,315]= 4/7875
Therefore, the GCF of 412/125,120/315 is 4/7875.
To find the highest common factor of 412,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 412,120 is 4.
Lets's calculate GCF of 412,120
2 | 412, 120 |
2 | 206, 60 |
103, 30 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 412,120 . The biggest common factor number is the GCF number.
So the greatest common factor 412,120 is 4.
Lets's calculate LCM of 125,315
5 | 125, 315 |
25, 63 |
∴ So the LCM of the given numbers is 5 x 25 x 63 = 7875
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/7875
Therefore, the GCF of Fractions 412/125,120/315 is 4/7875
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 125,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(125,315) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(125,315) x common factors =5 x 1 = 5
LCM(125,315) = ( 125 × 315 ) / 5
LCM(125,315) = 39375 / 5
LCM(125,315) = 7875
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 412,120?
The HCF of 412,120 is 4
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 412/125, 120/315?
Answer: GCF of Numerators as per given numbers 412/125, 120/315 is
GCF of Numerators i.e. for 412,120 is 4
LCM of denominators i.e. for 125,315 is 7875.
Thus, GCF of Fractions is 4/7875.Finally, GCF of Fractions for 412/125, 120/315 is 4/7875.