Use our free GCF of Fractions Calculator tool to compute the GCF of 471/897, 408/978 i.e 3/292422 easily. The following is the detailed procedure to determine the greatest common factor of fractions 471/897, 408/978.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 471/897,408/978
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 471/897,408/978, numerators are 471,408
Denominators are 897,978
The GCF of 471,408 is 3 .
LCM of 897,978 is 292422.
The greatest common factor of 471/897,408/978 = [GCF of 471,408]/[LCM of 897,978]= 3/292422
Therefore, the GCF of 471/897,408/978 is 3/292422.
To find the highest common factor of 471,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 471 are 1, 3, 157, 471
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 471,408 is 3.
Lets's calculate GCF of 471,408
3 | 471, 408 |
157, 136 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 471
:1,3,157,471
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 471,408 . The biggest common factor number is the GCF number.
So the greatest common factor 471,408 is 3.
Lets's calculate LCM of 897,978
3 | 897, 978 |
299, 326 |
∴ So the LCM of the given numbers is 3 x 299 x 326 = 292422
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/292422
Therefore, the GCF of Fractions 471/897,408/978 is 3/292422
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 897,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(897,978) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(897,978) x common factors =3 x 1 = 3
LCM(897,978) = ( 897 × 978 ) / 3
LCM(897,978) = 877266 / 3
LCM(897,978) = 292422
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 471,408?
The HCF of 471,408 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 471/897, 408/978?
Answer: GCF of Numerators as per given numbers 471/897, 408/978 is
GCF of Numerators i.e. for 471,408 is 3
LCM of denominators i.e. for 897,978 is 292422.
Thus, GCF of Fractions is 3/292422.Finally, GCF of Fractions for 471/897, 408/978 is 3/292422.