Use our free GCF of Fractions Calculator tool to compute the GCF of 284/130, 838/464 i.e 2/30160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/130, 838/464.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 284/130,838/464
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 284/130,838/464, numerators are 284,838
Denominators are 130,464
The GCF of 284,838 is 2 .
LCM of 130,464 is 30160.
The greatest common factor of 284/130,838/464 = [GCF of 284,838]/[LCM of 130,464]= 2/30160
Therefore, the GCF of 284/130,838/464 is 2/30160.
To find the highest common factor of 284,838, we have to find the factors of both numbers and list the highest common factor.
The factors of 284 are 1, 2, 4, 71, 142, 284
The factors of 838 are 1, 2, 419, 838
The HCF of 284,838 is 2.
Lets's calculate GCF of 284,838
2 | 284, 838 |
142, 419 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 284
:1,2,4,71,142,284
Now, list down the factors of 838
:1,2,419,838
Greatest Common Factor
We found the factors 284,838 . The biggest common factor number is the GCF number.
So the greatest common factor 284,838 is 2.
Lets's calculate LCM of 130,464
2 | 130, 464 |
65, 232 |
∴ So the LCM of the given numbers is 2 x 65 x 232 = 30160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30160
Therefore, the GCF of Fractions 284/130,838/464 is 2/30160
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 130,464 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(130,464) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(130,464) x common factors =2 x 1 = 2
LCM(130,464) = ( 130 × 464 ) / 2
LCM(130,464) = 60320 / 2
LCM(130,464) = 30160
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 284,838?
The HCF of 284,838 is 2
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 284/130, 838/464?
Answer: GCF of Numerators as per given numbers 284/130, 838/464 is
GCF of Numerators i.e. for 284,838 is 2
LCM of denominators i.e. for 130,464 is 30160.
Thus, GCF of Fractions is 2/30160.Finally, GCF of Fractions for 284/130, 838/464 is 2/30160.