Use our free GCF of Fractions Calculator tool to compute the GCF of 75/123, 45/960, 405/955 i.e 15/7517760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/123, 45/960, 405/955.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/123,45/960,405/955
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 75/123,45/960,405/955, numerators are 75,45,405
Denominators are 123,960,955
The GCF of 75,45,405 is 15 .
LCM of 123,960,955 is 7517760.
The greatest common factor of 75/123,45/960,405/955 = [GCF of 75,45,405]/[LCM of 123,960,955]= 15/7517760
Therefore, the GCF of 75/123,45/960,405/955 is 15/7517760.
To find the highest common factor of 75,45,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 75,45,405 is 15.
Lets's calculate GCF of 75,45,405
3 | 75, 45, 405 |
5 | 25, 15, 135 |
5, 3, 27 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 75,45,405 . The biggest common factor number is the GCF number.
So the greatest common factor 75,45,405 is 15.
Lets's calculate LCM of 123,960,955
3 | 123, 960, 955 |
5 | 41, 320, 955 |
41, 64, 191 |
∴ So the LCM of the given numbers is 3 x 5 x 41 x 64 x 191 = 7517760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/7517760
Therefore, the GCF of Fractions 75/123,45/960,405/955 is 15/7517760
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 123,960,955 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,960,955) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(123,960,955) x common factors =1 x 15 = 15
LCM(123,960,955) = ( 123 × 960 × 955 ) / 15
LCM(123,960,955) = 112766400 / 15
LCM(123,960,955) = 7517760
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 75,45,405?
The HCF of 75,45,405 is 15
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 75/123, 45/960, 405/955?
Answer: GCF of Numerators as per given numbers 75/123, 45/960, 405/955 is
GCF of Numerators i.e. for 75,45,405 is 15
LCM of denominators i.e. for 123,960,955 is 7517760.
Thus, GCF of Fractions is 15/7517760.Finally, GCF of Fractions for 75/123, 45/960, 405/955 is 15/7517760.