Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 45/405,138/276
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 45,138
Greatest Common Factor of Numerators i.e. GCF of 45,138 is 3 .
LCM of Denominators means LCM of 405,276 as per the given fractions.
LCM of 405,276 is 37260 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 45,138
3 | 45, 138 |
15, 46 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 138
List of positive integer factors of 138 that divides 138 without a remainder.
1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 45,138 . The biggest common factor number is the GCF number.
So the greatest common factor 45,138 is 3.
Lets's calculate LCM of 405,276
3 | 405, 276 |
135, 92 |
∴ So the LCM of the given numbers is 3 x 135 x 92 = 37260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/37260
Therefore, the GCF of Fractions 45/405,138/276 is 3/37260
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 405,276 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,276) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(405,276) x common factors =3 x 1 = 3
LCM(405,276) = ( 405 × 276 ) / 3
LCM(405,276) = 111780 / 3
LCM(405,276) = 37260
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 45/405, 138/276?
Answer: GCF of Numerators as per given numbers 45/405, 138/276 is
GCF of Numerators i.e. for 45,138 is 3
LCM of denominators i.e. for 405,276 is 37260.
Thus, GCF of Fractions is 3/37260.Finally, GCF of Fractions for 45/405, 138/276 is 3/37260.