Use our free GCF of Fractions Calculator tool to compute the GCF of 150/468, 140/384 i.e 10/14976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 150/468, 140/384.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 150/468,140/384
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 150/468,140/384, numerators are 150,140
Denominators are 468,384
The GCF of 150,140 is 10 .
LCM of 468,384 is 14976.
The greatest common factor of 150/468,140/384 = [GCF of 150,140]/[LCM of 468,384]= 10/14976
Therefore, the GCF of 150/468,140/384 is 10/14976.
To find the highest common factor of 150,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 150,140 is 10.
Lets's calculate GCF of 150,140
2 | 150, 140 |
5 | 75, 70 |
15, 14 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 150
:1,2,3,5,6,10,15,25,30,50,75,150
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 150,140 . The biggest common factor number is the GCF number.
So the greatest common factor 150,140 is 10.
Lets's calculate LCM of 468,384
2 | 468, 384 |
2 | 234, 192 |
3 | 117, 96 |
39, 32 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 39 x 32 = 14976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/14976
Therefore, the GCF of Fractions 150/468,140/384 is 10/14976
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 468,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(468,384) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(468,384) x common factors =12 x 1 = 12
LCM(468,384) = ( 468 × 384 ) / 12
LCM(468,384) = 179712 / 12
LCM(468,384) = 14976
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 150,140?
The HCF of 150,140 is 10
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 150/468, 140/384?
Answer: GCF of Numerators as per given numbers 150/468, 140/384 is
GCF of Numerators i.e. for 150,140 is 10
LCM of denominators i.e. for 468,384 is 14976.
Thus, GCF of Fractions is 10/14976.Finally, GCF of Fractions for 150/468, 140/384 is 10/14976.