Use our free GCF of Fractions Calculator tool to compute the GCF of 219/984, 288/746 i.e 3/367032 easily. The following is the detailed procedure to determine the greatest common factor of fractions 219/984, 288/746.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 219/984,288/746
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 219/984,288/746, numerators are 219,288
Denominators are 984,746
The GCF of 219,288 is 3 .
LCM of 984,746 is 367032.
The greatest common factor of 219/984,288/746 = [GCF of 219,288]/[LCM of 984,746]= 3/367032
Therefore, the GCF of 219/984,288/746 is 3/367032.
To find the highest common factor of 219,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 219 are 1, 3, 73, 219
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The HCF of 219,288 is 3.
Lets's calculate GCF of 219,288
3 | 219, 288 |
73, 96 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 219
:1,3,73,219
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Greatest Common Factor
We found the factors 219,288 . The biggest common factor number is the GCF number.
So the greatest common factor 219,288 is 3.
Lets's calculate LCM of 984,746
2 | 984, 746 |
492, 373 |
∴ So the LCM of the given numbers is 2 x 492 x 373 = 367032
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/367032
Therefore, the GCF of Fractions 219/984,288/746 is 3/367032
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 984,746 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(984,746) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(984,746) x common factors =2 x 1 = 2
LCM(984,746) = ( 984 × 746 ) / 2
LCM(984,746) = 734064 / 2
LCM(984,746) = 367032
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 219,288?
The HCF of 219,288 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 219/984, 288/746?
Answer: GCF of Numerators as per given numbers 219/984, 288/746 is
GCF of Numerators i.e. for 219,288 is 3
LCM of denominators i.e. for 984,746 is 367032.
Thus, GCF of Fractions is 3/367032.Finally, GCF of Fractions for 219/984, 288/746 is 3/367032.