Use our free GCF of Fractions Calculator tool to compute the GCF of 3/89, 9/10, 6/96, 81/480 i.e 3/42720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/89, 9/10, 6/96, 81/480.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3/89,9/10,6/96,81/480
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 3/89,9/10,6/96,81/480, numerators are 3,9,6,81
Denominators are 89,10,96,480
The GCF of 3,9,6,81 is 3 .
LCM of 89,10,96,480 is 42720.
The greatest common factor of 3/89,9/10,6/96,81/480 = [GCF of 3,9,6,81]/[LCM of 89,10,96,480]= 3/42720
Therefore, the GCF of 3/89,9/10,6/96,81/480 is 3/42720.
To find the highest common factor of 3,9,6,81, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 9 are 1, 3, 9
The factors of 6 are 1, 2, 3, 6
The factors of 81 are 1, 3, 9, 27, 81
The HCF of 3,9,6,81 is 3.
Lets's calculate GCF of 3,9,6,81
3 | 3, 9, 6, 81 |
1, 3, 2, 27 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 3
:1,3
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 81
:1,3,9,27,81
Greatest Common Factor
We found the factors 3,9,6,81 . The biggest common factor number is the GCF number.
So the greatest common factor 3,9,6,81 is 3.
Lets's calculate LCM of 89,10,96,480
2 | 89, 10, 96, 480 |
2 | 89, 5, 48, 240 |
2 | 89, 5, 24, 120 |
2 | 89, 5, 12, 60 |
2 | 89, 5, 6, 30 |
3 | 89, 5, 3, 15 |
5 | 89, 5, 1, 5 |
89, 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 89 x 1 x 1 x 1 = 42720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/42720
Therefore, the GCF of Fractions 3/89,9/10,6/96,81/480 is 3/42720
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 89,10,96,480 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(89,10,96,480) = 1
common factors(in case of two or more numbers have common factors) = 960
GCF(89,10,96,480) x common factors =1 x 960 = 960
LCM(89,10,96,480) = ( 89 × 10 × 96 × 480 ) / 960
LCM(89,10,96,480) = 41011200 / 960
LCM(89,10,96,480) = 42720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 3,9,6,81?
The HCF of 3,9,6,81 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 3/89, 9/10, 6/96, 81/480?
Answer: GCF of Numerators as per given numbers 3/89, 9/10, 6/96, 81/480 is
GCF of Numerators i.e. for 3,9,6,81 is 3
LCM of denominators i.e. for 89,10,96,480 is 42720.
Thus, GCF of Fractions is 3/42720.Finally, GCF of Fractions for 3/89, 9/10, 6/96, 81/480 is 3/42720.