Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 28/50,67/36,86/92,41/120
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 28,67,86,41
Greatest Common Factor of Numerators i.e. GCF of 28,67,86,41 is 1 .
LCM of Denominators means LCM of 50,36,92,120 as per the given fractions.
LCM of 50,36,92,120 is 41400 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 28,67,86,41
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1,2,43,86
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1,41
Greatest Common Factor
We found the factors 28,67,86,41 . The biggest common factor number is the GCF number.
So the greatest common factor 28,67,86,41 is 1.
Lets's calculate LCM of 50,36,92,120
2 | 50, 36, 92, 120 |
2 | 25, 18, 46, 60 |
3 | 25, 9, 23, 30 |
5 | 25, 3, 23, 10 |
5, 3, 23, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 5 x 3 x 23 x 2 = 41400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41400
Therefore, the GCF of Fractions 28/50,67/36,86/92,41/120 is 1/41400
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 50,36,92,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(50,36,92,120) = 2
common factors(in case of two or more numbers have common factors) = 240
GCF(50,36,92,120) x common factors =2 x 240 = 480
LCM(50,36,92,120) = ( 50 × 36 × 92 × 120 ) / 480
LCM(50,36,92,120) = 19872000 / 480
LCM(50,36,92,120) = 41400
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 28/50, 67/36, 86/92, 41/120?
Answer: GCF of Numerators as per given numbers 28/50, 67/36, 86/92, 41/120 is
GCF of Numerators i.e. for 28,67,86,41 is 1
LCM of denominators i.e. for 50,36,92,120 is 41400.
Thus, GCF of Fractions is 1/41400.Finally, GCF of Fractions for 28/50, 67/36, 86/92, 41/120 is 1/41400.