Use our free GCF of Fractions Calculator tool to compute the GCF of 68/306, 612/477, 498/318 i.e 2/16218 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/306, 612/477, 498/318.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/306,612/477,498/318
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 68/306,612/477,498/318, numerators are 68,612,498
Denominators are 306,477,318
The GCF of 68,612,498 is 2 .
LCM of 306,477,318 is 16218.
The greatest common factor of 68/306,612/477,498/318 = [GCF of 68,612,498]/[LCM of 306,477,318]= 2/16218
Therefore, the GCF of 68/306,612/477,498/318 is 2/16218.
To find the highest common factor of 68,612,498, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498
The HCF of 68,612,498 is 2.
Lets's calculate GCF of 68,612,498
2 | 68, 612, 498 |
34, 306, 249 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Now, list down the factors of 498
:1,2,3,6,83,166,249,498
Greatest Common Factor
We found the factors 68,612,498 . The biggest common factor number is the GCF number.
So the greatest common factor 68,612,498 is 2.
Lets's calculate LCM of 306,477,318
2 | 306, 477, 318 |
3 | 153, 477, 159 |
3 | 51, 53, 159 |
53 | 17, 53, 53 |
17, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 53 x 17 x 1 x 1 = 16218
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16218
Therefore, the GCF of Fractions 68/306,612/477,498/318 is 2/16218
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 306,477,318 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,477,318) = 3
common factors(in case of two or more numbers have common factors) = 954
GCF(306,477,318) x common factors =3 x 954 = 2862
LCM(306,477,318) = ( 306 × 477 × 318 ) / 2862
LCM(306,477,318) = 46415916 / 2862
LCM(306,477,318) = 16218
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 68,612,498?
The HCF of 68,612,498 is 2
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 68/306, 612/477, 498/318?
Answer: GCF of Numerators as per given numbers 68/306, 612/477, 498/318 is
GCF of Numerators i.e. for 68,612,498 is 2
LCM of denominators i.e. for 306,477,318 is 16218.
Thus, GCF of Fractions is 2/16218.Finally, GCF of Fractions for 68/306, 612/477, 498/318 is 2/16218.