Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/73,36/90,465/220
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 27,36,465
Greatest Common Factor of Numerators i.e. GCF of 27,36,465 is 3 .
LCM of Denominators means LCM of 73,90,220 as per the given fractions.
LCM of 73,90,220 is 144540 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 27,36,465
3 | 27, 36, 465 |
9, 12, 155 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 465
List of positive integer factors of 465 that divides 465 without a remainder.
1,3,5,15,31,93,155,465
Greatest Common Factor
We found the factors 27,36,465 . The biggest common factor number is the GCF number.
So the greatest common factor 27,36,465 is 3.
Lets's calculate LCM of 73,90,220
2 | 73, 90, 220 |
5 | 73, 45, 110 |
73, 9, 22 |
∴ So the LCM of the given numbers is 2 x 5 x 73 x 9 x 22 = 144540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/144540
Therefore, the GCF of Fractions 27/73,36/90,465/220 is 3/144540
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 73,90,220 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(73,90,220) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(73,90,220) x common factors =1 x 10 = 10
LCM(73,90,220) = ( 73 × 90 × 220 ) / 10
LCM(73,90,220) = 1445400 / 10
LCM(73,90,220) = 144540
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 27/73, 36/90, 465/220?
Answer: GCF of Numerators as per given numbers 27/73, 36/90, 465/220 is
GCF of Numerators i.e. for 27,36,465 is 3
LCM of denominators i.e. for 73,90,220 is 144540.
Thus, GCF of Fractions is 3/144540.Finally, GCF of Fractions for 27/73, 36/90, 465/220 is 3/144540.