Use our free GCF of Fractions Calculator tool to compute the GCF of 10/235, 170/157, 975/313 i.e 5/11548135 easily. The following is the detailed procedure to determine the greatest common factor of fractions 10/235, 170/157, 975/313.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 10/235,170/157,975/313
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 10/235,170/157,975/313, numerators are 10,170,975
Denominators are 235,157,313
The GCF of 10,170,975 is 5 .
LCM of 235,157,313 is 11548135.
The greatest common factor of 10/235,170/157,975/313 = [GCF of 10,170,975]/[LCM of 235,157,313]= 5/11548135
Therefore, the GCF of 10/235,170/157,975/313 is 5/11548135.
To find the highest common factor of 10,170,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 10 are 1, 2, 5, 10
The factors of 170 are 1, 2, 5, 10, 17, 34, 85, 170
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 10,170,975 is 5.
Lets's calculate GCF of 10,170,975
5 | 10, 170, 975 |
2, 34, 195 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 170
:1,2,5,10,17,34,85,170
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 10,170,975 . The biggest common factor number is the GCF number.
So the greatest common factor 10,170,975 is 5.
Lets's calculate LCM of 235,157,313
Given numbers has no common factors except 1. So, there LCM is their product i.e 11548135
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/11548135
Therefore, the GCF of Fractions 10/235,170/157,975/313 is 5/11548135
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 235,157,313 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(235,157,313) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(235,157,313) x common factors =1 x 1 = 1
LCM(235,157,313) = ( 235 × 157 × 313 ) / 1
LCM(235,157,313) = 11548135 / 1
LCM(235,157,313) = 11548135
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 10,170,975?
The HCF of 10,170,975 is 5
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 10/235, 170/157, 975/313?
Answer: GCF of Numerators as per given numbers 10/235, 170/157, 975/313 is
GCF of Numerators i.e. for 10,170,975 is 5
LCM of denominators i.e. for 235,157,313 is 11548135.
Thus, GCF of Fractions is 5/11548135.Finally, GCF of Fractions for 10/235, 170/157, 975/313 is 5/11548135.