Use our free GCF of Fractions Calculator tool to compute the GCF of 810/856, 342/352 i.e 18/37664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/856, 342/352.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 810/856,342/352
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 810/856,342/352, numerators are 810,342
Denominators are 856,352
The GCF of 810,342 is 18 .
LCM of 856,352 is 37664.
The greatest common factor of 810/856,342/352 = [GCF of 810,342]/[LCM of 856,352]= 18/37664
Therefore, the GCF of 810/856,342/352 is 18/37664.
To find the highest common factor of 810,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 810,342 is 18.
Lets's calculate GCF of 810,342
2 | 810, 342 |
3 | 405, 171 |
3 | 135, 57 |
45, 19 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 810,342 . The biggest common factor number is the GCF number.
So the greatest common factor 810,342 is 18.
Lets's calculate LCM of 856,352
2 | 856, 352 |
2 | 428, 176 |
2 | 214, 88 |
107, 44 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 107 x 44 = 37664
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/37664
Therefore, the GCF of Fractions 810/856,342/352 is 18/37664
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 856,352 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(856,352) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(856,352) x common factors =8 x 1 = 8
LCM(856,352) = ( 856 × 352 ) / 8
LCM(856,352) = 301312 / 8
LCM(856,352) = 37664
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 810,342?
The HCF of 810,342 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 810/856, 342/352?
Answer: GCF of Numerators as per given numbers 810/856, 342/352 is
GCF of Numerators i.e. for 810,342 is 18
LCM of denominators i.e. for 856,352 is 37664.
Thus, GCF of Fractions is 18/37664.Finally, GCF of Fractions for 810/856, 342/352 is 18/37664.