Use our free GCF of Fractions Calculator tool to compute the GCF of 82/894, 69/344, 167/678 i.e 1/17375784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/894, 69/344, 167/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/894,69/344,167/678
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 82/894,69/344,167/678, numerators are 82,69,167
Denominators are 894,344,678
The GCF of 82,69,167 is 1 .
LCM of 894,344,678 is 17375784.
The greatest common factor of 82/894,69/344,167/678 = [GCF of 82,69,167]/[LCM of 894,344,678]= 1/17375784
Therefore, the GCF of 82/894,69/344,167/678 is 1/17375784.
To find the highest common factor of 82,69,167, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 69 are 1, 3, 23, 69
The factors of 167 are 1, 167
The HCF of 82,69,167 is 1.
Lets's calculate GCF of 82,69,167
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 167
:1,167
Greatest Common Factor
We found the factors 82,69,167 . The biggest common factor number is the GCF number.
So the greatest common factor 82,69,167 is 1.
Lets's calculate LCM of 894,344,678
2 | 894, 344, 678 |
3 | 447, 172, 339 |
149, 172, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 149 x 172 x 113 = 17375784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17375784
Therefore, the GCF of Fractions 82/894,69/344,167/678 is 1/17375784
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 894,344,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(894,344,678) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(894,344,678) x common factors =2 x 6 = 12
LCM(894,344,678) = ( 894 × 344 × 678 ) / 12
LCM(894,344,678) = 208509408 / 12
LCM(894,344,678) = 17375784
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 82,69,167?
The HCF of 82,69,167 is 1
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 82/894, 69/344, 167/678?
Answer: GCF of Numerators as per given numbers 82/894, 69/344, 167/678 is
GCF of Numerators i.e. for 82,69,167 is 1
LCM of denominators i.e. for 894,344,678 is 17375784.
Thus, GCF of Fractions is 1/17375784.Finally, GCF of Fractions for 82/894, 69/344, 167/678 is 1/17375784.