Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 74/49,20/55,14/55,96/14
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 74,20,14,96
Greatest Common Factor of Numerators i.e. GCF of 74,20,14,96 is 2 .
LCM of Denominators means LCM of 49,55,55,14 as per the given fractions.
LCM of 49,55,55,14 is 5390 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 74,20,14,96
2 | 74, 20, 14, 96 |
37, 10, 7, 48 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
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
Greatest Common Factor
We found the factors 74,20,14,96 . The biggest common factor number is the GCF number.
So the greatest common factor 74,20,14,96 is 2.
Lets's calculate LCM of 49,55,55,14
5 | 49, 55, 55, 14 |
7 | 49, 11, 11, 14 |
11 | 7, 11, 11, 2 |
7, 1, 1, 2 |
∴ So the LCM of the given numbers is 5 x 7 x 11 x 7 x 1 x 1 x 2 = 5390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5390
Therefore, the GCF of Fractions 74/49,20/55,14/55,96/14 is 2/5390
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 49,55,55,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,55,55,14) = 1
common factors(in case of two or more numbers have common factors) = 385
GCF(49,55,55,14) x common factors =1 x 385 = 385
LCM(49,55,55,14) = ( 49 × 55 × 55 × 14 ) / 385
LCM(49,55,55,14) = 2075150 / 385
LCM(49,55,55,14) = 5390
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 74/49, 20/55, 14/55, 96/14?
Answer: GCF of Numerators as per given numbers 74/49, 20/55, 14/55, 96/14 is
GCF of Numerators i.e. for 74,20,14,96 is 2
LCM of denominators i.e. for 49,55,55,14 is 5390.
Thus, GCF of Fractions is 2/5390.Finally, GCF of Fractions for 74/49, 20/55, 14/55, 96/14 is 2/5390.