Use our free GCF of Fractions Calculator tool to compute the GCF of 96/76, 58/15, 684/96 i.e 2/9120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/76, 58/15, 684/96.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 96/76,58/15,684/96
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 96/76,58/15,684/96, numerators are 96,58,684
Denominators are 76,15,96
The GCF of 96,58,684 is 2 .
LCM of 76,15,96 is 9120.
The greatest common factor of 96/76,58/15,684/96 = [GCF of 96,58,684]/[LCM of 76,15,96]= 2/9120
Therefore, the GCF of 96/76,58/15,684/96 is 2/9120.
To find the highest common factor of 96,58,684, 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 58 are 1, 2, 29, 58
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 96,58,684 is 2.
Lets's calculate GCF of 96,58,684
2 | 96, 58, 684 |
48, 29, 342 |
∴ 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 58
:1,2,29,58
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 96,58,684 . The biggest common factor number is the GCF number.
So the greatest common factor 96,58,684 is 2.
Lets's calculate LCM of 76,15,96
2 | 76, 15, 96 |
2 | 38, 15, 48 |
3 | 19, 15, 24 |
19, 5, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 5 x 8 = 9120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9120
Therefore, the GCF of Fractions 96/76,58/15,684/96 is 2/9120
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 76,15,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,15,96) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(76,15,96) x common factors =1 x 12 = 12
LCM(76,15,96) = ( 76 × 15 × 96 ) / 12
LCM(76,15,96) = 109440 / 12
LCM(76,15,96) = 9120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 96,58,684?
The HCF of 96,58,684 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 96/76, 58/15, 684/96?
Answer: GCF of Numerators as per given numbers 96/76, 58/15, 684/96 is
GCF of Numerators i.e. for 96,58,684 is 2
LCM of denominators i.e. for 76,15,96 is 9120.
Thus, GCF of Fractions is 2/9120.Finally, GCF of Fractions for 96/76, 58/15, 684/96 is 2/9120.