Use our free GCF of Fractions Calculator tool to compute the GCF of 209/324, 608/868 i.e 19/70308 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/324, 608/868.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 209/324,608/868
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 209/324,608/868, numerators are 209,608
Denominators are 324,868
The GCF of 209,608 is 19 .
LCM of 324,868 is 70308.
The greatest common factor of 209/324,608/868 = [GCF of 209,608]/[LCM of 324,868]= 19/70308
Therefore, the GCF of 209/324,608/868 is 19/70308.
To find the highest common factor of 209,608, we have to find the factors of both numbers and list the highest common factor.
The factors of 209 are 1, 11, 19, 209
The factors of 608 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608
The HCF of 209,608 is 19.
Lets's calculate GCF of 209,608
19 | 209, 608 |
11, 32 |
∴ So the GCF of the given numbers is 19 = 19
Now, list down the factors of 209
:1,11,19,209
Now, list down the factors of 608
:1,2,4,8,16,19,32,38,76,152,304,608
Greatest Common Factor
We found the factors 209,608 . The biggest common factor number is the GCF number.
So the greatest common factor 209,608 is 19.
Lets's calculate LCM of 324,868
2 | 324, 868 |
2 | 162, 434 |
81, 217 |
∴ So the LCM of the given numbers is 2 x 2 x 81 x 217 = 70308
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/70308
Therefore, the GCF of Fractions 209/324,608/868 is 19/70308
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 324,868 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,868) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(324,868) x common factors =4 x 1 = 4
LCM(324,868) = ( 324 × 868 ) / 4
LCM(324,868) = 281232 / 4
LCM(324,868) = 70308
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 209,608?
The HCF of 209,608 is 19
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 209/324, 608/868?
Answer: GCF of Numerators as per given numbers 209/324, 608/868 is
GCF of Numerators i.e. for 209,608 is 19
LCM of denominators i.e. for 324,868 is 70308.
Thus, GCF of Fractions is 19/70308.Finally, GCF of Fractions for 209/324, 608/868 is 19/70308.