Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 96/8,93/8,56/1,10/2,306/4,47/6,49/1,932/6,40/1,73/8
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 96,93,56,10,306,47,49,932,40,73
Greatest Common Factor of Numerators i.e. GCF of 96,93,56,10,306,47,49,932,40,73 is 1 .
LCM of Denominators means LCM of 8,8,1,2,4,6,1,6,1,8 as per the given fractions.
LCM of 8,8,1,2,4,6,1,6,1,8 is 24 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 96,93,56,10,306,47,49,932,40,73
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,96
Factors of 93
List of positive integer factors of 93 that divides 93 without a remainder.
1,3,31,93
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1,2,4,7,8,14,28,56
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Factors of 306
List of positive integer factors of 306 that divides 306 without a remainder.
1,2,3,6,9,17,18,34,51,102,153,306
Factors of 47
List of positive integer factors of 47 that divides 47 without a remainder.
1,47
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 932
List of positive integer factors of 932 that divides 932 without a remainder.
1,2,4,233,466,932
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 73
List of positive integer factors of 73 that divides 73 without a remainder.
1,73
Greatest Common Factor
We found the factors 96,93,56,10,306,47,49,932,40,73 . The biggest common factor number is the GCF number.
So the greatest common factor 96,93,56,10,306,47,49,932,40,73 is 1.
Lets's calculate LCM of 8,8,1,2,4,6,1,6,1,8
2 | 8, 8, 1, 2, 4, 6, 1, 6, 1, 8 |
2 | 4, 4, 1, 1, 2, 3, 1, 3, 1, 4 |
2 | 1, 2, 1, 1, 2, 3, 1, 3, 1, 2 |
3 | 1, 1, 1, 1, 1, 3, 1, 3, 1, 1 |
1, 1, 1, 1, 1, 1, 1, 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 24
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24
Therefore, the GCF of Fractions 96/8,93/8,56/1,10/2,306/4,47/6,49/1,932/6,40/1,73/8 is 1/24
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 8,8,1,2,4,6,1,6,1,8 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(8,8,1,2,4,6,1,6,1,8) = 1
common factors(in case of two or more numbers have common factors) = 6144
GCF(8,8,1,2,4,6,1,6,1,8) x common factors =1 x 6144 = 6144
LCM(8,8,1,2,4,6,1,6,1,8) = ( 8 × 8 × 1 × 2 × 4 × 6 × 1 × 6 × 1 × 8 ) / 6144
LCM(8,8,1,2,4,6,1,6,1,8) = 147456 / 6144
LCM(8,8,1,2,4,6,1,6,1,8) = 24
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 96/8, 93/8, 56/1, 10/2, 306/4, 47/6, 49/1, 932/6, 40/1, 73/8?
Answer: GCF of Numerators as per given numbers 96/8, 93/8, 56/1, 10/2, 306/4, 47/6, 49/1, 932/6, 40/1, 73/8 is
GCF of Numerators i.e. for 96,93,56,10,306,47,49,932,40,73 is 1
LCM of denominators i.e. for 8,8,1,2,4,6,1,6,1,8 is 24.
Thus, GCF of Fractions is 1/24.Finally, GCF of Fractions for 96/8, 93/8, 56/1, 10/2, 306/4, 47/6, 49/1, 932/6, 40/1, 73/8 is 1/24.