Use our free GCF of Fractions Calculator tool to compute the GCF of 384/577, 282/416 i.e 6/240032 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/577, 282/416.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 384/577,282/416
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 384/577,282/416, numerators are 384,282
Denominators are 577,416
The GCF of 384,282 is 6 .
LCM of 577,416 is 240032.
The greatest common factor of 384/577,282/416 = [GCF of 384,282]/[LCM of 577,416]= 6/240032
Therefore, the GCF of 384/577,282/416 is 6/240032.
To find the highest common factor of 384,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 384,282 is 6.
Lets's calculate GCF of 384,282
2 | 384, 282 |
3 | 192, 141 |
64, 47 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 384,282 . The biggest common factor number is the GCF number.
So the greatest common factor 384,282 is 6.
Lets's calculate LCM of 577,416
Given numbers has no common factors except 1. So, there LCM is their product i.e 240032
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/240032
Therefore, the GCF of Fractions 384/577,282/416 is 6/240032
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 577,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(577,416) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(577,416) x common factors =1 x 1 = 1
LCM(577,416) = ( 577 × 416 ) / 1
LCM(577,416) = 240032 / 1
LCM(577,416) = 240032
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 384,282?
The HCF of 384,282 is 6
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 384/577, 282/416?
Answer: GCF of Numerators as per given numbers 384/577, 282/416 is
GCF of Numerators i.e. for 384,282 is 6
LCM of denominators i.e. for 577,416 is 240032.
Thus, GCF of Fractions is 6/240032.Finally, GCF of Fractions for 384/577, 282/416 is 6/240032.