Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/70,83/45,33/99,31/914
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 27,83,33,31
Greatest Common Factor of Numerators i.e. GCF of 27,83,33,31 is 1 .
LCM of Denominators means LCM of 70,45,99,914 as per the given fractions.
LCM of 70,45,99,914 is 3167010 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 27,83,33,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Greatest Common Factor
We found the factors 27,83,33,31 . The biggest common factor number is the GCF number.
So the greatest common factor 27,83,33,31 is 1.
Lets's calculate LCM of 70,45,99,914
2 | 70, 45, 99, 914 |
3 | 35, 45, 99, 457 |
3 | 35, 15, 33, 457 |
5 | 35, 5, 11, 457 |
7, 1, 11, 457 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 7 x 1 x 11 x 457 = 3167010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3167010
Therefore, the GCF of Fractions 27/70,83/45,33/99,31/914 is 1/3167010
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 70,45,99,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,45,99,914) = 1
common factors(in case of two or more numbers have common factors) = 90
GCF(70,45,99,914) x common factors =1 x 90 = 90
LCM(70,45,99,914) = ( 70 × 45 × 99 × 914 ) / 90
LCM(70,45,99,914) = 285030900 / 90
LCM(70,45,99,914) = 3167010
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 27/70, 83/45, 33/99, 31/914?
Answer: GCF of Numerators as per given numbers 27/70, 83/45, 33/99, 31/914 is
GCF of Numerators i.e. for 27,83,33,31 is 1
LCM of denominators i.e. for 70,45,99,914 is 3167010.
Thus, GCF of Fractions is 1/3167010.Finally, GCF of Fractions for 27/70, 83/45, 33/99, 31/914 is 1/3167010.