Use our free GCF of Fractions Calculator tool to compute the GCF of 9/72, 9/45, 6/11, 18/218 i.e 3/431640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9/72, 9/45, 6/11, 18/218.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/72,9/45,6/11,18/218
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 9/72,9/45,6/11,18/218, numerators are 9,9,6,18
Denominators are 72,45,11,218
The GCF of 9,9,6,18 is 3 .
LCM of 72,45,11,218 is 431640.
The greatest common factor of 9/72,9/45,6/11,18/218 = [GCF of 9,9,6,18]/[LCM of 72,45,11,218]= 3/431640
Therefore, the GCF of 9/72,9/45,6/11,18/218 is 3/431640.
To find the highest common factor of 9,9,6,18, we have to find the factors of both numbers and list the highest common factor.
The factors of 9 are 1, 3, 9
The factors of 9 are 1, 3, 9
The factors of 6 are 1, 2, 3, 6
The factors of 18 are 1, 2, 3, 6, 9, 18
The HCF of 9,9,6,18 is 3.
Lets's calculate GCF of 9,9,6,18
3 | 9, 9, 6, 18 |
3, 3, 2, 6 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 18
:1,2,3,6,9,18
Greatest Common Factor
We found the factors 9,9,6,18 . The biggest common factor number is the GCF number.
So the greatest common factor 9,9,6,18 is 3.
Lets's calculate LCM of 72,45,11,218
2 | 72, 45, 11, 218 |
3 | 36, 45, 11, 109 |
3 | 12, 15, 11, 109 |
4, 5, 11, 109 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 4 x 5 x 11 x 109 = 431640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/431640
Therefore, the GCF of Fractions 9/72,9/45,6/11,18/218 is 3/431640
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 72,45,11,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,45,11,218) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(72,45,11,218) x common factors =1 x 18 = 18
LCM(72,45,11,218) = ( 72 × 45 × 11 × 218 ) / 18
LCM(72,45,11,218) = 7769520 / 18
LCM(72,45,11,218) = 431640
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 9,9,6,18?
The HCF of 9,9,6,18 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 9/72, 9/45, 6/11, 18/218?
Answer: GCF of Numerators as per given numbers 9/72, 9/45, 6/11, 18/218 is
GCF of Numerators i.e. for 9,9,6,18 is 3
LCM of denominators i.e. for 72,45,11,218 is 431640.
Thus, GCF of Fractions is 3/431640.Finally, GCF of Fractions for 9/72, 9/45, 6/11, 18/218 is 3/431640.