Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/26,40/40,80/75,64/197
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 13,40,80,64
Greatest Common Factor of Numerators i.e. GCF of 13,40,80,64 is 1 .
LCM of Denominators means LCM of 26,40,75,197 as per the given fractions.
LCM of 26,40,75,197 is 1536600 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 13,40,80,64
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 13
List of positive integer factors of 13 that divides 13 without a remainder.
1,13
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
Greatest Common Factor
We found the factors 13,40,80,64 . The biggest common factor number is the GCF number.
So the greatest common factor 13,40,80,64 is 1.
Lets's calculate LCM of 26,40,75,197
2 | 26, 40, 75, 197 |
5 | 13, 20, 75, 197 |
13, 4, 15, 197 |
∴ So the LCM of the given numbers is 2 x 5 x 13 x 4 x 15 x 197 = 1536600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1536600
Therefore, the GCF of Fractions 13/26,40/40,80/75,64/197 is 1/1536600
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 26,40,75,197 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(26,40,75,197) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(26,40,75,197) x common factors =1 x 10 = 10
LCM(26,40,75,197) = ( 26 × 40 × 75 × 197 ) / 10
LCM(26,40,75,197) = 15366000 / 10
LCM(26,40,75,197) = 1536600
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 13/26, 40/40, 80/75, 64/197?
Answer: GCF of Numerators as per given numbers 13/26, 40/40, 80/75, 64/197 is
GCF of Numerators i.e. for 13,40,80,64 is 1
LCM of denominators i.e. for 26,40,75,197 is 1536600.
Thus, GCF of Fractions is 1/1536600.Finally, GCF of Fractions for 13/26, 40/40, 80/75, 64/197 is 1/1536600.