Use our free GCF of Fractions Calculator tool to compute the GCF of 729/274, 162/472 i.e 81/64664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 729/274, 162/472.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 729/274,162/472
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 729/274,162/472, numerators are 729,162
Denominators are 274,472
The GCF of 729,162 is 81 .
LCM of 274,472 is 64664.
The greatest common factor of 729/274,162/472 = [GCF of 729,162]/[LCM of 274,472]= 81/64664
Therefore, the GCF of 729/274,162/472 is 81/64664.
To find the highest common factor of 729,162, we have to find the factors of both numbers and list the highest common factor.
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The HCF of 729,162 is 81.
Lets's calculate GCF of 729,162
3 | 729, 162 |
3 | 243, 54 |
3 | 81, 18 |
3 | 27, 6 |
9, 2 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 3 = 81
Now, list down the factors of 729
:1,3,9,27,81,243,729
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Greatest Common Factor
We found the factors 729,162 . The biggest common factor number is the GCF number.
So the greatest common factor 729,162 is 81.
Lets's calculate LCM of 274,472
2 | 274, 472 |
137, 236 |
∴ So the LCM of the given numbers is 2 x 137 x 236 = 64664
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 81/64664
Therefore, the GCF of Fractions 729/274,162/472 is 81/64664
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 274,472 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,472) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,472) x common factors =2 x 1 = 2
LCM(274,472) = ( 274 × 472 ) / 2
LCM(274,472) = 129328 / 2
LCM(274,472) = 64664
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 729,162?
The HCF of 729,162 is 81
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 729/274, 162/472?
Answer: GCF of Numerators as per given numbers 729/274, 162/472 is
GCF of Numerators i.e. for 729,162 is 81
LCM of denominators i.e. for 274,472 is 64664.
Thus, GCF of Fractions is 81/64664.Finally, GCF of Fractions for 729/274, 162/472 is 81/64664.