Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/96,96/96,36/49,15/140
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 54,96,36,15
Greatest Common Factor of Numerators i.e. GCF of 54,96,36,15 is 3 .
LCM of Denominators means LCM of 96,96,49,140 as per the given fractions.
LCM of 96,96,49,140 is 23520 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 54,96,36,15
3 | 54, 96, 36, 15 |
18, 32, 12, 5 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
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 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1,3,5,15
Greatest Common Factor
We found the factors 54,96,36,15 . The biggest common factor number is the GCF number.
So the greatest common factor 54,96,36,15 is 3.
Lets's calculate LCM of 96,96,49,140
2 | 96, 96, 49, 140 |
2 | 48, 48, 49, 70 |
2 | 24, 24, 49, 35 |
2 | 12, 12, 49, 35 |
2 | 6, 6, 49, 35 |
3 | 3, 3, 49, 35 |
7 | 1, 1, 49, 35 |
1, 1, 7, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 7 x 1 x 1 x 7 x 5 = 23520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/23520
Therefore, the GCF of Fractions 54/96,96/96,36/49,15/140 is 3/23520
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 96,96,49,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,96,49,140) = 1
common factors(in case of two or more numbers have common factors) = 2688
GCF(96,96,49,140) x common factors =1 x 2688 = 2688
LCM(96,96,49,140) = ( 96 × 96 × 49 × 140 ) / 2688
LCM(96,96,49,140) = 63221760 / 2688
LCM(96,96,49,140) = 23520
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 54/96, 96/96, 36/49, 15/140?
Answer: GCF of Numerators as per given numbers 54/96, 96/96, 36/49, 15/140 is
GCF of Numerators i.e. for 54,96,36,15 is 3
LCM of denominators i.e. for 96,96,49,140 is 23520.
Thus, GCF of Fractions is 3/23520.Finally, GCF of Fractions for 54/96, 96/96, 36/49, 15/140 is 3/23520.