Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 138/232,162/385
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 138,162
Greatest Common Factor of Numerators i.e. GCF of 138,162 is 6 .
LCM of Denominators means LCM of 232,385 as per the given fractions.
LCM of 232,385 is 89320 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 138,162
2 | 138, 162 |
3 | 69, 81 |
23, 27 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Factors of 138
List of positive integer factors of 138 that divides 138 without a remainder.
1,2,3,6,23,46,69,138
Factors of 162
List of positive integer factors of 162 that divides 162 without a remainder.
1,2,3,6,9,18,27,54,81,162
Greatest Common Factor
We found the factors 138,162 . The biggest common factor number is the GCF number.
So the greatest common factor 138,162 is 6.
Lets's calculate LCM of 232,385
Given numbers has no common factors except 1. So, there LCM is their product i.e 89320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/89320
Therefore, the GCF of Fractions 138/232,162/385 is 6/89320
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 232,385 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(232,385) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(232,385) x common factors =1 x 1 = 1
LCM(232,385) = ( 232 × 385 ) / 1
LCM(232,385) = 89320 / 1
LCM(232,385) = 89320
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 138/232, 162/385?
Answer: GCF of Numerators as per given numbers 138/232, 162/385 is
GCF of Numerators i.e. for 138,162 is 6
LCM of denominators i.e. for 232,385 is 89320.
Thus, GCF of Fractions is 6/89320.Finally, GCF of Fractions for 138/232, 162/385 is 6/89320.