Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 11/51,10/90,17/81,30/385
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 11,10,17,30
Greatest Common Factor of Numerators i.e. GCF of 11,10,17,30 is 1 .
LCM of Denominators means LCM of 51,90,81,385 as per the given fractions.
LCM of 51,90,81,385 is 1060290 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 11,10,17,30
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 11
List of positive integer factors of 11 that divides 11 without a remainder.
1,11
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Greatest Common Factor
We found the factors 11,10,17,30 . The biggest common factor number is the GCF number.
So the greatest common factor 11,10,17,30 is 1.
Lets's calculate LCM of 51,90,81,385
3 | 51, 90, 81, 385 |
3 | 17, 30, 27, 385 |
5 | 17, 10, 9, 385 |
17, 2, 9, 77 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 17 x 2 x 9 x 77 = 1060290
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1060290
Therefore, the GCF of Fractions 11/51,10/90,17/81,30/385 is 1/1060290
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 51,90,81,385 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,90,81,385) = 1
common factors(in case of two or more numbers have common factors) = 135
GCF(51,90,81,385) x common factors =1 x 135 = 135
LCM(51,90,81,385) = ( 51 × 90 × 81 × 385 ) / 135
LCM(51,90,81,385) = 143139150 / 135
LCM(51,90,81,385) = 1060290
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 11/51, 10/90, 17/81, 30/385?
Answer: GCF of Numerators as per given numbers 11/51, 10/90, 17/81, 30/385 is
GCF of Numerators i.e. for 11,10,17,30 is 1
LCM of denominators i.e. for 51,90,81,385 is 1060290.
Thus, GCF of Fractions is 1/1060290.Finally, GCF of Fractions for 11/51, 10/90, 17/81, 30/385 is 1/1060290.