Use our free GCF of Fractions Calculator tool to compute the GCF of 305/57, 690/961 i.e 5/54777 easily. The following is the detailed procedure to determine the greatest common factor of fractions 305/57, 690/961.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 305/57,690/961
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 305/57,690/961, numerators are 305,690
Denominators are 57,961
The GCF of 305,690 is 5 .
LCM of 57,961 is 54777.
The greatest common factor of 305/57,690/961 = [GCF of 305,690]/[LCM of 57,961]= 5/54777
Therefore, the GCF of 305/57,690/961 is 5/54777.
To find the highest common factor of 305,690, we have to find the factors of both numbers and list the highest common factor.
The factors of 305 are 1, 5, 61, 305
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The HCF of 305,690 is 5.
Lets's calculate GCF of 305,690
5 | 305, 690 |
61, 138 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 305
:1,5,61,305
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Greatest Common Factor
We found the factors 305,690 . The biggest common factor number is the GCF number.
So the greatest common factor 305,690 is 5.
Lets's calculate LCM of 57,961
Given numbers has no common factors except 1. So, there LCM is their product i.e 54777
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/54777
Therefore, the GCF of Fractions 305/57,690/961 is 5/54777
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 57,961 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,961) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(57,961) x common factors =1 x 1 = 1
LCM(57,961) = ( 57 × 961 ) / 1
LCM(57,961) = 54777 / 1
LCM(57,961) = 54777
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 305,690?
The HCF of 305,690 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 305/57, 690/961?
Answer: GCF of Numerators as per given numbers 305/57, 690/961 is
GCF of Numerators i.e. for 305,690 is 5
LCM of denominators i.e. for 57,961 is 54777.
Thus, GCF of Fractions is 5/54777.Finally, GCF of Fractions for 305/57, 690/961 is 5/54777.