Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 43/96,75/17,22/56,69/426
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 43,75,22,69
Greatest Common Factor of Numerators i.e. GCF of 43,75,22,69 is 1 .
LCM of Denominators means LCM of 96,17,56,426 as per the given fractions.
LCM of 96,17,56,426 is 811104 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 43,75,22,69
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Greatest Common Factor
We found the factors 43,75,22,69 . The biggest common factor number is the GCF number.
So the greatest common factor 43,75,22,69 is 1.
Lets's calculate LCM of 96,17,56,426
2 | 96, 17, 56, 426 |
2 | 48, 17, 28, 213 |
2 | 24, 17, 14, 213 |
3 | 12, 17, 7, 213 |
4, 17, 7, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 4 x 17 x 7 x 71 = 811104
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/811104
Therefore, the GCF of Fractions 43/96,75/17,22/56,69/426 is 1/811104
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 96,17,56,426 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,17,56,426) = 1
common factors(in case of two or more numbers have common factors) = 48
GCF(96,17,56,426) x common factors =1 x 48 = 48
LCM(96,17,56,426) = ( 96 × 17 × 56 × 426 ) / 48
LCM(96,17,56,426) = 38932992 / 48
LCM(96,17,56,426) = 811104
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 43/96, 75/17, 22/56, 69/426?
Answer: GCF of Numerators as per given numbers 43/96, 75/17, 22/56, 69/426 is
GCF of Numerators i.e. for 43,75,22,69 is 1
LCM of denominators i.e. for 96,17,56,426 is 811104.
Thus, GCF of Fractions is 1/811104.Finally, GCF of Fractions for 43/96, 75/17, 22/56, 69/426 is 1/811104.