Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/56,48/20,35/35,18/13
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 72,48,35,18
Greatest Common Factor of Numerators i.e. GCF of 72,48,35,18 is 1 .
LCM of Denominators means LCM of 56,20,35,13 as per the given fractions.
LCM of 56,20,35,13 is 3640 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 72,48,35,18
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 48
List of positive integer factors of 48 that divides 48 without a remainder.
1,2,3,4,6,8,12,16,24,48
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Greatest Common Factor
We found the factors 72,48,35,18 . The biggest common factor number is the GCF number.
So the greatest common factor 72,48,35,18 is 1.
Lets's calculate LCM of 56,20,35,13
2 | 56, 20, 35, 13 |
2 | 28, 10, 35, 13 |
5 | 14, 5, 35, 13 |
7 | 14, 1, 7, 13 |
2, 1, 1, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 2 x 1 x 1 x 13 = 3640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3640
Therefore, the GCF of Fractions 72/56,48/20,35/35,18/13 is 1/3640
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 56,20,35,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,20,35,13) = 1
common factors(in case of two or more numbers have common factors) = 140
GCF(56,20,35,13) x common factors =1 x 140 = 140
LCM(56,20,35,13) = ( 56 × 20 × 35 × 13 ) / 140
LCM(56,20,35,13) = 509600 / 140
LCM(56,20,35,13) = 3640
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 72/56, 48/20, 35/35, 18/13?
Answer: GCF of Numerators as per given numbers 72/56, 48/20, 35/35, 18/13 is
GCF of Numerators i.e. for 72,48,35,18 is 1
LCM of denominators i.e. for 56,20,35,13 is 3640.
Thus, GCF of Fractions is 1/3640.Finally, GCF of Fractions for 72/56, 48/20, 35/35, 18/13 is 1/3640.