Use our free GCF of Fractions Calculator tool to compute the GCF of 824/205, 468/971 i.e 4/199055 easily. The following is the detailed procedure to determine the greatest common factor of fractions 824/205, 468/971.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 824/205,468/971
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 824/205,468/971, numerators are 824,468
Denominators are 205,971
The GCF of 824,468 is 4 .
LCM of 205,971 is 199055.
The greatest common factor of 824/205,468/971 = [GCF of 824,468]/[LCM of 205,971]= 4/199055
Therefore, the GCF of 824/205,468/971 is 4/199055.
To find the highest common factor of 824,468, we have to find the factors of both numbers and list the highest common factor.
The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The HCF of 824,468 is 4.
Lets's calculate GCF of 824,468
2 | 824, 468 |
2 | 412, 234 |
206, 117 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 824
:1,2,4,8,103,206,412,824
Now, list down the factors of 468
:1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468
Greatest Common Factor
We found the factors 824,468 . The biggest common factor number is the GCF number.
So the greatest common factor 824,468 is 4.
Lets's calculate LCM of 205,971
Given numbers has no common factors except 1. So, there LCM is their product i.e 199055
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/199055
Therefore, the GCF of Fractions 824/205,468/971 is 4/199055
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 205,971 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,971) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,971) x common factors =1 x 1 = 1
LCM(205,971) = ( 205 × 971 ) / 1
LCM(205,971) = 199055 / 1
LCM(205,971) = 199055
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 824,468?
The HCF of 824,468 is 4
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 824/205, 468/971?
Answer: GCF of Numerators as per given numbers 824/205, 468/971 is
GCF of Numerators i.e. for 824,468 is 4
LCM of denominators i.e. for 205,971 is 199055.
Thus, GCF of Fractions is 4/199055.Finally, GCF of Fractions for 824/205, 468/971 is 4/199055.