Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/13,42/13,867/56
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 21,42,867
Greatest Common Factor of Numerators i.e. GCF of 21,42,867 is 3 .
LCM of Denominators means LCM of 13,13,56 as per the given fractions.
LCM of 13,13,56 is 728 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 21,42,867
3 | 21, 42, 867 |
7, 14, 289 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 867
List of positive integer factors of 867 that divides 867 without a remainder.
1,3,17,51,289,867
Greatest Common Factor
We found the factors 21,42,867 . The biggest common factor number is the GCF number.
So the greatest common factor 21,42,867 is 3.
Lets's calculate LCM of 13,13,56
13 | 13, 13, 56 |
1, 1, 56 |
∴ So the LCM of the given numbers is 13 x 1 x 1 x 56 = 728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/728
Therefore, the GCF of Fractions 21/13,42/13,867/56 is 3/728
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 13,13,56 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,13,56) = 1
common factors(in case of two or more numbers have common factors) = 13
GCF(13,13,56) x common factors =1 x 13 = 13
LCM(13,13,56) = ( 13 × 13 × 56 ) / 13
LCM(13,13,56) = 9464 / 13
LCM(13,13,56) = 728
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 21/13, 42/13, 867/56?
Answer: GCF of Numerators as per given numbers 21/13, 42/13, 867/56 is
GCF of Numerators i.e. for 21,42,867 is 3
LCM of denominators i.e. for 13,13,56 is 728.
Thus, GCF of Fractions is 3/728.Finally, GCF of Fractions for 21/13, 42/13, 867/56 is 3/728.