Use our free GCF of Fractions Calculator tool to compute the GCF of 27/76, 210/84, 258/994 i.e 3/113316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/76, 210/84, 258/994.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/76,210/84,258/994
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 27/76,210/84,258/994, numerators are 27,210,258
Denominators are 76,84,994
The GCF of 27,210,258 is 3 .
LCM of 76,84,994 is 113316.
The greatest common factor of 27/76,210/84,258/994 = [GCF of 27,210,258]/[LCM of 76,84,994]= 3/113316
Therefore, the GCF of 27/76,210/84,258/994 is 3/113316.
To find the highest common factor of 27,210,258, we have to find the factors of both numbers and list the highest common factor.
The factors of 27 are 1, 3, 9, 27
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 258 are 1, 2, 3, 6, 43, 86, 129, 258
The HCF of 27,210,258 is 3.
Lets's calculate GCF of 27,210,258
3 | 27, 210, 258 |
9, 70, 86 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Now, list down the factors of 258
:1,2,3,6,43,86,129,258
Greatest Common Factor
We found the factors 27,210,258 . The biggest common factor number is the GCF number.
So the greatest common factor 27,210,258 is 3.
Lets's calculate LCM of 76,84,994
2 | 76, 84, 994 |
2 | 38, 42, 497 |
7 | 19, 21, 497 |
19, 3, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 19 x 3 x 71 = 113316
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/113316
Therefore, the GCF of Fractions 27/76,210/84,258/994 is 3/113316
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 76,84,994 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,84,994) = 2
common factors(in case of two or more numbers have common factors) = 28
GCF(76,84,994) x common factors =2 x 28 = 56
LCM(76,84,994) = ( 76 × 84 × 994 ) / 56
LCM(76,84,994) = 6345696 / 56
LCM(76,84,994) = 113316
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 27,210,258?
The HCF of 27,210,258 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 27/76, 210/84, 258/994?
Answer: GCF of Numerators as per given numbers 27/76, 210/84, 258/994 is
GCF of Numerators i.e. for 27,210,258 is 3
LCM of denominators i.e. for 76,84,994 is 113316.
Thus, GCF of Fractions is 3/113316.Finally, GCF of Fractions for 27/76, 210/84, 258/994 is 3/113316.