Use our free GCF of Fractions Calculator tool to compute the GCF of 426/365, 240/275 i.e 6/20075 easily. The following is the detailed procedure to determine the greatest common factor of fractions 426/365, 240/275.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 426/365,240/275
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 426/365,240/275, numerators are 426,240
Denominators are 365,275
The GCF of 426,240 is 6 .
LCM of 365,275 is 20075.
The greatest common factor of 426/365,240/275 = [GCF of 426,240]/[LCM of 365,275]= 6/20075
Therefore, the GCF of 426/365,240/275 is 6/20075.
To find the highest common factor of 426,240, we have to find the factors of both numbers and list the highest common factor.
The factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The HCF of 426,240 is 6.
Lets's calculate GCF of 426,240
2 | 426, 240 |
3 | 213, 120 |
71, 40 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 426
:1,2,3,6,71,142,213,426
Now, list down the factors of 240
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240
Greatest Common Factor
We found the factors 426,240 . The biggest common factor number is the GCF number.
So the greatest common factor 426,240 is 6.
Lets's calculate LCM of 365,275
5 | 365, 275 |
73, 55 |
∴ So the LCM of the given numbers is 5 x 73 x 55 = 20075
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/20075
Therefore, the GCF of Fractions 426/365,240/275 is 6/20075
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 365,275 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(365,275) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(365,275) x common factors =5 x 1 = 5
LCM(365,275) = ( 365 × 275 ) / 5
LCM(365,275) = 100375 / 5
LCM(365,275) = 20075
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 426,240?
The HCF of 426,240 is 6
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 426/365, 240/275?
Answer: GCF of Numerators as per given numbers 426/365, 240/275 is
GCF of Numerators i.e. for 426,240 is 6
LCM of denominators i.e. for 365,275 is 20075.
Thus, GCF of Fractions is 6/20075.Finally, GCF of Fractions for 426/365, 240/275 is 6/20075.