Use our free GCF of Fractions Calculator tool to compute the GCF of 724/723, 832/582 i.e 4/140262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 724/723, 832/582.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 724/723,832/582
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 724/723,832/582, numerators are 724,832
Denominators are 723,582
The GCF of 724,832 is 4 .
LCM of 723,582 is 140262.
The greatest common factor of 724/723,832/582 = [GCF of 724,832]/[LCM of 723,582]= 4/140262
Therefore, the GCF of 724/723,832/582 is 4/140262.
To find the highest common factor of 724,832, we have to find the factors of both numbers and list the highest common factor.
The factors of 724 are 1, 2, 4, 181, 362, 724
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The HCF of 724,832 is 4.
Lets's calculate GCF of 724,832
2 | 724, 832 |
2 | 362, 416 |
181, 208 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 724
:1,2,4,181,362,724
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
Greatest Common Factor
We found the factors 724,832 . The biggest common factor number is the GCF number.
So the greatest common factor 724,832 is 4.
Lets's calculate LCM of 723,582
3 | 723, 582 |
241, 194 |
∴ So the LCM of the given numbers is 3 x 241 x 194 = 140262
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/140262
Therefore, the GCF of Fractions 724/723,832/582 is 4/140262
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 723,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,582) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(723,582) x common factors =3 x 1 = 3
LCM(723,582) = ( 723 × 582 ) / 3
LCM(723,582) = 420786 / 3
LCM(723,582) = 140262
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 724,832?
The HCF of 724,832 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 724/723, 832/582?
Answer: GCF of Numerators as per given numbers 724/723, 832/582 is
GCF of Numerators i.e. for 724,832 is 4
LCM of denominators i.e. for 723,582 is 140262.
Thus, GCF of Fractions is 4/140262.Finally, GCF of Fractions for 724/723, 832/582 is 4/140262.