Use our free GCF of Fractions Calculator tool to compute the GCF of 86/135, 18/240, 461/180 i.e 1/2160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/135, 18/240, 461/180.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 86/135,18/240,461/180
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 86/135,18/240,461/180, numerators are 86,18,461
Denominators are 135,240,180
The GCF of 86,18,461 is 1 .
LCM of 135,240,180 is 2160.
The greatest common factor of 86/135,18/240,461/180 = [GCF of 86,18,461]/[LCM of 135,240,180]= 1/2160
Therefore, the GCF of 86/135,18/240,461/180 is 1/2160.
To find the highest common factor of 86,18,461, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 461 are 1, 461
The HCF of 86,18,461 is 1.
Lets's calculate GCF of 86,18,461
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 18
:1,2,3,6,9,18
Now, list down the factors of 461
:1,461
Greatest Common Factor
We found the factors 86,18,461 . The biggest common factor number is the GCF number.
So the greatest common factor 86,18,461 is 1.
Lets's calculate LCM of 135,240,180
2 | 135, 240, 180 |
2 | 135, 120, 90 |
3 | 135, 60, 45 |
3 | 15, 20, 45 |
5 | 5, 20, 15 |
1, 4, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 1 x 4 x 3 = 2160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2160
Therefore, the GCF of Fractions 86/135,18/240,461/180 is 1/2160
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 135,240,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(135,240,180) = 15
common factors(in case of two or more numbers have common factors) = 180
GCF(135,240,180) x common factors =15 x 180 = 2700
LCM(135,240,180) = ( 135 × 240 × 180 ) / 2700
LCM(135,240,180) = 5832000 / 2700
LCM(135,240,180) = 2160
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 86,18,461?
The HCF of 86,18,461 is 1
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 86/135, 18/240, 461/180?
Answer: GCF of Numerators as per given numbers 86/135, 18/240, 461/180 is
GCF of Numerators i.e. for 86,18,461 is 1
LCM of denominators i.e. for 135,240,180 is 2160.
Thus, GCF of Fractions is 1/2160.Finally, GCF of Fractions for 86/135, 18/240, 461/180 is 1/2160.