Use our free GCF of Fractions Calculator tool to compute the GCF of 96/820, 54/410, 490/240 i.e 2/9840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/820, 54/410, 490/240.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 96/820,54/410,490/240
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 96/820,54/410,490/240, numerators are 96,54,490
Denominators are 820,410,240
The GCF of 96,54,490 is 2 .
LCM of 820,410,240 is 9840.
The greatest common factor of 96/820,54/410,490/240 = [GCF of 96,54,490]/[LCM of 820,410,240]= 2/9840
Therefore, the GCF of 96/820,54/410,490/240 is 2/9840.
To find the highest common factor of 96,54,490, we have to find the factors of both numbers and list the highest common factor.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The HCF of 96,54,490 is 2.
Lets's calculate GCF of 96,54,490
2 | 96, 54, 490 |
48, 27, 245 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 490
:1,2,5,7,10,14,35,49,70,98,245,490
Greatest Common Factor
We found the factors 96,54,490 . The biggest common factor number is the GCF number.
So the greatest common factor 96,54,490 is 2.
Lets's calculate LCM of 820,410,240
2 | 820, 410, 240 |
2 | 410, 205, 120 |
5 | 205, 205, 60 |
41 | 41, 41, 12 |
1, 1, 12 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 41 x 1 x 1 x 12 = 9840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9840
Therefore, the GCF of Fractions 96/820,54/410,490/240 is 2/9840
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 820,410,240 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(820,410,240) = 10
common factors(in case of two or more numbers have common factors) = 820
GCF(820,410,240) x common factors =10 x 820 = 8200
LCM(820,410,240) = ( 820 × 410 × 240 ) / 8200
LCM(820,410,240) = 80688000 / 8200
LCM(820,410,240) = 9840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 96,54,490?
The HCF of 96,54,490 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 96/820, 54/410, 490/240?
Answer: GCF of Numerators as per given numbers 96/820, 54/410, 490/240 is
GCF of Numerators i.e. for 96,54,490 is 2
LCM of denominators i.e. for 820,410,240 is 9840.
Thus, GCF of Fractions is 2/9840.Finally, GCF of Fractions for 96/820, 54/410, 490/240 is 2/9840.