Use our free GCF of Fractions Calculator tool to compute the GCF of 990/750, 288/759 i.e 18/189750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 990/750, 288/759.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 990/750,288/759
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 990/750,288/759, numerators are 990,288
Denominators are 750,759
The GCF of 990,288 is 18 .
LCM of 750,759 is 189750.
The greatest common factor of 990/750,288/759 = [GCF of 990,288]/[LCM of 750,759]= 18/189750
Therefore, the GCF of 990/750,288/759 is 18/189750.
To find the highest common factor of 990,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
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 990,288 is 18.
Lets's calculate GCF of 990,288
2 | 990, 288 |
3 | 495, 144 |
3 | 165, 48 |
55, 16 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 990
:1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990
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 990,288 . The biggest common factor number is the GCF number.
So the greatest common factor 990,288 is 18.
Lets's calculate LCM of 750,759
3 | 750, 759 |
250, 253 |
∴ So the LCM of the given numbers is 3 x 250 x 253 = 189750
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/189750
Therefore, the GCF of Fractions 990/750,288/759 is 18/189750
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 750,759 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(750,759) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(750,759) x common factors =3 x 1 = 3
LCM(750,759) = ( 750 × 759 ) / 3
LCM(750,759) = 569250 / 3
LCM(750,759) = 189750
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 990,288?
The HCF of 990,288 is 18
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 990/750, 288/759?
Answer: GCF of Numerators as per given numbers 990/750, 288/759 is
GCF of Numerators i.e. for 990,288 is 18
LCM of denominators i.e. for 750,759 is 189750.
Thus, GCF of Fractions is 18/189750.Finally, GCF of Fractions for 990/750, 288/759 is 18/189750.