Use our free GCF of Fractions Calculator tool to compute the GCF of 966/361, 219/972 i.e 3/350892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 966/361, 219/972.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 966/361,219/972
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 966/361,219/972, numerators are 966,219
Denominators are 361,972
The GCF of 966,219 is 3 .
LCM of 361,972 is 350892.
The greatest common factor of 966/361,219/972 = [GCF of 966,219]/[LCM of 361,972]= 3/350892
Therefore, the GCF of 966/361,219/972 is 3/350892.
To find the highest common factor of 966,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
The factors of 219 are 1, 3, 73, 219
The HCF of 966,219 is 3.
Lets's calculate GCF of 966,219
3 | 966, 219 |
322, 73 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 966
:1,2,3,6,7,14,21,23,42,46,69,138,161,322,483,966
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 966,219 . The biggest common factor number is the GCF number.
So the greatest common factor 966,219 is 3.
Lets's calculate LCM of 361,972
Given numbers has no common factors except 1. So, there LCM is their product i.e 350892
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/350892
Therefore, the GCF of Fractions 966/361,219/972 is 3/350892
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 361,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(361,972) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(361,972) x common factors =1 x 1 = 1
LCM(361,972) = ( 361 × 972 ) / 1
LCM(361,972) = 350892 / 1
LCM(361,972) = 350892
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 966,219?
The HCF of 966,219 is 3
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 966/361, 219/972?
Answer: GCF of Numerators as per given numbers 966/361, 219/972 is
GCF of Numerators i.e. for 966,219 is 3
LCM of denominators i.e. for 361,972 is 350892.
Thus, GCF of Fractions is 3/350892.Finally, GCF of Fractions for 966/361, 219/972 is 3/350892.