Use our free GCF of Fractions Calculator tool to compute the GCF of 447/576, 978/567 i.e 3/36288 easily. The following is the detailed procedure to determine the greatest common factor of fractions 447/576, 978/567.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 447/576,978/567
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 447/576,978/567, numerators are 447,978
Denominators are 576,567
The GCF of 447,978 is 3 .
LCM of 576,567 is 36288.
The greatest common factor of 447/576,978/567 = [GCF of 447,978]/[LCM of 576,567]= 3/36288
Therefore, the GCF of 447/576,978/567 is 3/36288.
To find the highest common factor of 447,978, we have to find the factors of both numbers and list the highest common factor.
The factors of 447 are 1, 3, 149, 447
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The HCF of 447,978 is 3.
Lets's calculate GCF of 447,978
3 | 447, 978 |
149, 326 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 447
:1,3,149,447
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Greatest Common Factor
We found the factors 447,978 . The biggest common factor number is the GCF number.
So the greatest common factor 447,978 is 3.
Lets's calculate LCM of 576,567
3 | 576, 567 |
3 | 192, 189 |
64, 63 |
∴ So the LCM of the given numbers is 3 x 3 x 64 x 63 = 36288
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/36288
Therefore, the GCF of Fractions 447/576,978/567 is 3/36288
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 576,567 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(576,567) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(576,567) x common factors =9 x 1 = 9
LCM(576,567) = ( 576 × 567 ) / 9
LCM(576,567) = 326592 / 9
LCM(576,567) = 36288
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 447,978?
The HCF of 447,978 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 447/576, 978/567?
Answer: GCF of Numerators as per given numbers 447/576, 978/567 is
GCF of Numerators i.e. for 447,978 is 3
LCM of denominators i.e. for 576,567 is 36288.
Thus, GCF of Fractions is 3/36288.Finally, GCF of Fractions for 447/576, 978/567 is 3/36288.