Use our free GCF of Fractions Calculator tool to compute the GCF of 408/570, 296/618 i.e 8/58710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/570, 296/618.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 408/570,296/618
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 408/570,296/618, numerators are 408,296
Denominators are 570,618
The GCF of 408,296 is 8 .
LCM of 570,618 is 58710.
The greatest common factor of 408/570,296/618 = [GCF of 408,296]/[LCM of 570,618]= 8/58710
Therefore, the GCF of 408/570,296/618 is 8/58710.
To find the highest common factor of 408,296, we have to find the factors of both numbers and list the highest common factor.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296
The HCF of 408,296 is 8.
Lets's calculate GCF of 408,296
2 | 408, 296 |
2 | 204, 148 |
2 | 102, 74 |
51, 37 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 296
:1,2,4,8,37,74,148,296
Greatest Common Factor
We found the factors 408,296 . The biggest common factor number is the GCF number.
So the greatest common factor 408,296 is 8.
Lets's calculate LCM of 570,618
2 | 570, 618 |
3 | 285, 309 |
95, 103 |
∴ So the LCM of the given numbers is 2 x 3 x 95 x 103 = 58710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/58710
Therefore, the GCF of Fractions 408/570,296/618 is 8/58710
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 570,618 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(570,618) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(570,618) x common factors =6 x 1 = 6
LCM(570,618) = ( 570 × 618 ) / 6
LCM(570,618) = 352260 / 6
LCM(570,618) = 58710
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 408,296?
The HCF of 408,296 is 8
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 408/570, 296/618?
Answer: GCF of Numerators as per given numbers 408/570, 296/618 is
GCF of Numerators i.e. for 408,296 is 8
LCM of denominators i.e. for 570,618 is 58710.
Thus, GCF of Fractions is 8/58710.Finally, GCF of Fractions for 408/570, 296/618 is 8/58710.