Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 232/65,766/40,742/214
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 232,766,742
Greatest Common Factor of Numerators i.e. GCF of 232,766,742 is 2 .
LCM of Denominators means LCM of 65,40,214 as per the given fractions.
LCM of 65,40,214 is 55640 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 232,766,742
2 | 232, 766, 742 |
116, 383, 371 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 232
List of positive integer factors of 232 that divides 232 without a remainder.
1,2,4,8,29,58,116,232
Factors of 766
List of positive integer factors of 766 that divides 766 without a remainder.
1,2,383,766
Factors of 742
List of positive integer factors of 742 that divides 742 without a remainder.
1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 232,766,742 . The biggest common factor number is the GCF number.
So the greatest common factor 232,766,742 is 2.
Lets's calculate LCM of 65,40,214
2 | 65, 40, 214 |
5 | 65, 20, 107 |
13, 4, 107 |
∴ So the LCM of the given numbers is 2 x 5 x 13 x 4 x 107 = 55640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/55640
Therefore, the GCF of Fractions 232/65,766/40,742/214 is 2/55640
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 65,40,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,40,214) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(65,40,214) x common factors =1 x 10 = 10
LCM(65,40,214) = ( 65 × 40 × 214 ) / 10
LCM(65,40,214) = 556400 / 10
LCM(65,40,214) = 55640
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 232/65, 766/40, 742/214?
Answer: GCF of Numerators as per given numbers 232/65, 766/40, 742/214 is
GCF of Numerators i.e. for 232,766,742 is 2
LCM of denominators i.e. for 65,40,214 is 55640.
Thus, GCF of Fractions is 2/55640.Finally, GCF of Fractions for 232/65, 766/40, 742/214 is 2/55640.