Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 32/74,38/36,27/80,117/60
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 32,38,27,117
Greatest Common Factor of Numerators i.e. GCF of 32,38,27,117 is 1 .
LCM of Denominators means LCM of 74,36,80,60 as per the given fractions.
LCM of 74,36,80,60 is 26640 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 32,38,27,117
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 38
List of positive integer factors of 38 that divides 38 without a remainder.
1,2,19,38
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 117
List of positive integer factors of 117 that divides 117 without a remainder.
1,3,9,13,39,117
Greatest Common Factor
We found the factors 32,38,27,117 . The biggest common factor number is the GCF number.
So the greatest common factor 32,38,27,117 is 1.
Lets's calculate LCM of 74,36,80,60
2 | 74, 36, 80, 60 |
2 | 37, 18, 40, 30 |
3 | 37, 9, 20, 15 |
5 | 37, 3, 20, 5 |
37, 3, 4, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 37 x 3 x 4 x 1 = 26640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26640
Therefore, the GCF of Fractions 32/74,38/36,27/80,117/60 is 1/26640
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 74,36,80,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,36,80,60) = 2
common factors(in case of two or more numbers have common factors) = 240
GCF(74,36,80,60) x common factors =2 x 240 = 480
LCM(74,36,80,60) = ( 74 × 36 × 80 × 60 ) / 480
LCM(74,36,80,60) = 12787200 / 480
LCM(74,36,80,60) = 26640
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 32/74, 38/36, 27/80, 117/60?
Answer: GCF of Numerators as per given numbers 32/74, 38/36, 27/80, 117/60 is
GCF of Numerators i.e. for 32,38,27,117 is 1
LCM of denominators i.e. for 74,36,80,60 is 26640.
Thus, GCF of Fractions is 1/26640.Finally, GCF of Fractions for 32/74, 38/36, 27/80, 117/60 is 1/26640.