Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 756/132,6842/1689
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 756,6842
Greatest Common Factor of Numerators i.e. GCF of 756,6842 is 2 .
LCM of Denominators means LCM of 132,1689 as per the given fractions.
LCM of 132,1689 is 74316 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 756,6842
2 | 756, 6842 |
378, 3421 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 756
List of positive integer factors of 756 that divides 756 without a remainder.
1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Factors of 6842
List of positive integer factors of 6842 that divides 6842 without a remainder.
1,2,11,22,311,622,3421,6842
Greatest Common Factor
We found the factors 756,6842 . The biggest common factor number is the GCF number.
So the greatest common factor 756,6842 is 2.
Lets's calculate LCM of 132,1689
3 | 132, 1689 |
44, 563 |
∴ So the LCM of the given numbers is 3 x 44 x 563 = 74316
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/74316
Therefore, the GCF of Fractions 756/132,6842/1689 is 2/74316
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 132,1689 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,1689) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(132,1689) x common factors =3 x 1 = 3
LCM(132,1689) = ( 132 × 1689 ) / 3
LCM(132,1689) = 222948 / 3
LCM(132,1689) = 74316
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 756/132, 6842/1689?
Answer: GCF of Numerators as per given numbers 756/132, 6842/1689 is
GCF of Numerators i.e. for 756,6842 is 2
LCM of denominators i.e. for 132,1689 is 74316.
Thus, GCF of Fractions is 2/74316.Finally, GCF of Fractions for 756/132, 6842/1689 is 2/74316.