Use our free GCF of Fractions Calculator tool to compute the GCF of 54/857, 20/282, 408/916 i.e 2/110686692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/857, 20/282, 408/916.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/857,20/282,408/916
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 54/857,20/282,408/916, numerators are 54,20,408
Denominators are 857,282,916
The GCF of 54,20,408 is 2 .
LCM of 857,282,916 is 110686692.
The greatest common factor of 54/857,20/282,408/916 = [GCF of 54,20,408]/[LCM of 857,282,916]= 2/110686692
Therefore, the GCF of 54/857,20/282,408/916 is 2/110686692.
To find the highest common factor of 54,20,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 54,20,408 is 2.
Lets's calculate GCF of 54,20,408
2 | 54, 20, 408 |
27, 10, 204 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 54,20,408 . The biggest common factor number is the GCF number.
So the greatest common factor 54,20,408 is 2.
Lets's calculate LCM of 857,282,916
2 | 857, 282, 916 |
857, 141, 458 |
∴ So the LCM of the given numbers is 2 x 857 x 141 x 458 = 110686692
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/110686692
Therefore, the GCF of Fractions 54/857,20/282,408/916 is 2/110686692
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 857,282,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(857,282,916) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(857,282,916) x common factors =1 x 2 = 2
LCM(857,282,916) = ( 857 × 282 × 916 ) / 2
LCM(857,282,916) = 221373384 / 2
LCM(857,282,916) = 110686692
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 54,20,408?
The HCF of 54,20,408 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 54/857, 20/282, 408/916?
Answer: GCF of Numerators as per given numbers 54/857, 20/282, 408/916 is
GCF of Numerators i.e. for 54,20,408 is 2
LCM of denominators i.e. for 857,282,916 is 110686692.
Thus, GCF of Fractions is 2/110686692.Finally, GCF of Fractions for 54/857, 20/282, 408/916 is 2/110686692.