Use our free GCF of Fractions Calculator tool to compute the GCF of 831/160, 542/584 i.e 1/11680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 831/160, 542/584.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 831/160,542/584
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 831/160,542/584, numerators are 831,542
Denominators are 160,584
The GCF of 831,542 is 1 .
LCM of 160,584 is 11680.
The greatest common factor of 831/160,542/584 = [GCF of 831,542]/[LCM of 160,584]= 1/11680
Therefore, the GCF of 831/160,542/584 is 1/11680.
To find the highest common factor of 831,542, we have to find the factors of both numbers and list the highest common factor.
The factors of 831 are 1, 3, 277, 831
The factors of 542 are 1, 2, 271, 542
The HCF of 831,542 is 1.
Lets's calculate GCF of 831,542
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 831
:1,3,277,831
Now, list down the factors of 542
:1,2,271,542
Greatest Common Factor
We found the factors 831,542 . The biggest common factor number is the GCF number.
So the greatest common factor 831,542 is 1.
Lets's calculate LCM of 160,584
2 | 160, 584 |
2 | 80, 292 |
2 | 40, 146 |
20, 73 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 20 x 73 = 11680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11680
Therefore, the GCF of Fractions 831/160,542/584 is 1/11680
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 160,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(160,584) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(160,584) x common factors =8 x 1 = 8
LCM(160,584) = ( 160 × 584 ) / 8
LCM(160,584) = 93440 / 8
LCM(160,584) = 11680
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 831,542?
The HCF of 831,542 is 1
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 831/160, 542/584?
Answer: GCF of Numerators as per given numbers 831/160, 542/584 is
GCF of Numerators i.e. for 831,542 is 1
LCM of denominators i.e. for 160,584 is 11680.
Thus, GCF of Fractions is 1/11680.Finally, GCF of Fractions for 831/160, 542/584 is 1/11680.