Use our free GCF of Fractions Calculator tool to compute the GCF of 75/217, 60/8160 i.e 15/1770720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/217, 60/8160.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/217,60/8160
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 75/217,60/8160, numerators are 75,60
Denominators are 217,8160
The GCF of 75,60 is 15 .
LCM of 217,8160 is 1770720.
The greatest common factor of 75/217,60/8160 = [GCF of 75,60]/[LCM of 217,8160]= 15/1770720
Therefore, the GCF of 75/217,60/8160 is 15/1770720.
To find the highest common factor of 75,60, 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 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The HCF of 75,60 is 15.
Lets's calculate GCF of 75,60
3 | 75, 60 |
5 | 25, 20 |
5, 4 |
∴ 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 60
:1,2,3,4,5,6,10,12,15,20,30,60
Greatest Common Factor
We found the factors 75,60 . The biggest common factor number is the GCF number.
So the greatest common factor 75,60 is 15.
Lets's calculate LCM of 217,8160
Given numbers has no common factors except 1. So, there LCM is their product i.e 1770720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/1770720
Therefore, the GCF of Fractions 75/217,60/8160 is 15/1770720
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 217,8160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,8160) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,8160) x common factors =1 x 1 = 1
LCM(217,8160) = ( 217 × 8160 ) / 1
LCM(217,8160) = 1770720 / 1
LCM(217,8160) = 1770720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 75,60?
The HCF of 75,60 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 75/217, 60/8160?
Answer: GCF of Numerators as per given numbers 75/217, 60/8160 is
GCF of Numerators i.e. for 75,60 is 15
LCM of denominators i.e. for 217,8160 is 1770720.
Thus, GCF of Fractions is 15/1770720.Finally, GCF of Fractions for 75/217, 60/8160 is 15/1770720.