Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/30,84/43,764/23
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 69,84,764
Greatest Common Factor of Numerators i.e. GCF of 69,84,764 is 1 .
LCM of Denominators means LCM of 30,43,23 as per the given fractions.
LCM of 30,43,23 is 29670 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 69,84,764
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 764
List of positive integer factors of 764 that divides 764 without a remainder.
1,2,4,191,382,764
Greatest Common Factor
We found the factors 69,84,764 . The biggest common factor number is the GCF number.
So the greatest common factor 69,84,764 is 1.
Lets's calculate LCM of 30,43,23
Given numbers has no common factors except 1. So, there LCM is their product i.e 29670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29670
Therefore, the GCF of Fractions 69/30,84/43,764/23 is 1/29670
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 30,43,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,43,23) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(30,43,23) x common factors =1 x 1 = 1
LCM(30,43,23) = ( 30 × 43 × 23 ) / 1
LCM(30,43,23) = 29670 / 1
LCM(30,43,23) = 29670
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 69/30, 84/43, 764/23?
Answer: GCF of Numerators as per given numbers 69/30, 84/43, 764/23 is
GCF of Numerators i.e. for 69,84,764 is 1
LCM of denominators i.e. for 30,43,23 is 29670.
Thus, GCF of Fractions is 1/29670.Finally, GCF of Fractions for 69/30, 84/43, 764/23 is 1/29670.