Use our free GCF of Fractions Calculator tool to compute the GCF of 855/234, 513/308 i.e 171/36036 easily. The following is the detailed procedure to determine the greatest common factor of fractions 855/234, 513/308.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 855/234,513/308
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 855/234,513/308, numerators are 855,513
Denominators are 234,308
The GCF of 855,513 is 171 .
LCM of 234,308 is 36036.
The greatest common factor of 855/234,513/308 = [GCF of 855,513]/[LCM of 234,308]= 171/36036
Therefore, the GCF of 855/234,513/308 is 171/36036.
To find the highest common factor of 855,513, we have to find the factors of both numbers and list the highest common factor.
The factors of 855 are 1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The HCF of 855,513 is 171.
Lets's calculate GCF of 855,513
3 | 855, 513 |
3 | 285, 171 |
19 | 95, 57 |
5, 3 |
∴ So the GCF of the given numbers is 3 x 3 x 19 = 171
Now, list down the factors of 855
:1,3,5,9,15,19,45,57,95,171,285,855
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Greatest Common Factor
We found the factors 855,513 . The biggest common factor number is the GCF number.
So the greatest common factor 855,513 is 171.
Lets's calculate LCM of 234,308
2 | 234, 308 |
117, 154 |
∴ So the LCM of the given numbers is 2 x 117 x 154 = 36036
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 171/36036
Therefore, the GCF of Fractions 855/234,513/308 is 171/36036
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 234,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(234,308) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(234,308) x common factors =2 x 1 = 2
LCM(234,308) = ( 234 × 308 ) / 2
LCM(234,308) = 72072 / 2
LCM(234,308) = 36036
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 855,513?
The HCF of 855,513 is 171
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 855/234, 513/308?
Answer: GCF of Numerators as per given numbers 855/234, 513/308 is
GCF of Numerators i.e. for 855,513 is 171
LCM of denominators i.e. for 234,308 is 36036.
Thus, GCF of Fractions is 171/36036.Finally, GCF of Fractions for 855/234, 513/308 is 171/36036.