Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/134,180/122
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 36,180
Greatest Common Factor of Numerators i.e. GCF of 36,180 is 36 .
LCM of Denominators means LCM of 134,122 as per the given fractions.
LCM of 134,122 is 8174 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 36,180
2 | 36, 180 |
2 | 18, 90 |
3 | 9, 45 |
3 | 3, 15 |
1, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
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 180
List of positive integer factors of 180 that divides 180 without a remainder.
1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Greatest Common Factor
We found the factors 36,180 . The biggest common factor number is the GCF number.
So the greatest common factor 36,180 is 36.
Lets's calculate LCM of 134,122
2 | 134, 122 |
67, 61 |
∴ So the LCM of the given numbers is 2 x 67 x 61 = 8174
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/8174
Therefore, the GCF of Fractions 36/134,180/122 is 36/8174
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 134,122 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(134,122) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(134,122) x common factors =2 x 1 = 2
LCM(134,122) = ( 134 × 122 ) / 2
LCM(134,122) = 16348 / 2
LCM(134,122) = 8174
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 36/134, 180/122?
Answer: GCF of Numerators as per given numbers 36/134, 180/122 is
GCF of Numerators i.e. for 36,180 is 36
LCM of denominators i.e. for 134,122 is 8174.
Thus, GCF of Fractions is 36/8174.Finally, GCF of Fractions for 36/134, 180/122 is 36/8174.