Use our free GCF of Fractions Calculator tool to compute the GCF of 232/584, 184/976 i.e 8/71248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 232/584, 184/976.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 232/584,184/976
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 232/584,184/976, numerators are 232,184
Denominators are 584,976
The GCF of 232,184 is 8 .
LCM of 584,976 is 71248.
The greatest common factor of 232/584,184/976 = [GCF of 232,184]/[LCM of 584,976]= 8/71248
Therefore, the GCF of 232/584,184/976 is 8/71248.
To find the highest common factor of 232,184, we have to find the factors of both numbers and list the highest common factor.
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232
The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184
The HCF of 232,184 is 8.
Lets's calculate GCF of 232,184
2 | 232, 184 |
2 | 116, 92 |
2 | 58, 46 |
29, 23 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 232
:1,2,4,8,29,58,116,232
Now, list down the factors of 184
:1,2,4,8,23,46,92,184
Greatest Common Factor
We found the factors 232,184 . The biggest common factor number is the GCF number.
So the greatest common factor 232,184 is 8.
Lets's calculate LCM of 584,976
2 | 584, 976 |
2 | 292, 488 |
2 | 146, 244 |
73, 122 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 73 x 122 = 71248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/71248
Therefore, the GCF of Fractions 232/584,184/976 is 8/71248
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 584,976 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(584,976) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(584,976) x common factors =8 x 1 = 8
LCM(584,976) = ( 584 × 976 ) / 8
LCM(584,976) = 569984 / 8
LCM(584,976) = 71248
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 232,184?
The HCF of 232,184 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 232/584, 184/976?
Answer: GCF of Numerators as per given numbers 232/584, 184/976 is
GCF of Numerators i.e. for 232,184 is 8
LCM of denominators i.e. for 584,976 is 71248.
Thus, GCF of Fractions is 8/71248.Finally, GCF of Fractions for 232/584, 184/976 is 8/71248.