Use our free GCF of Fractions Calculator tool to compute the GCF of 23/20, 15/69, 186/78 i.e 1/17940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/20, 15/69, 186/78.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 23/20,15/69,186/78
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 23/20,15/69,186/78, numerators are 23,15,186
Denominators are 20,69,78
The GCF of 23,15,186 is 1 .
LCM of 20,69,78 is 17940.
The greatest common factor of 23/20,15/69,186/78 = [GCF of 23,15,186]/[LCM of 20,69,78]= 1/17940
Therefore, the GCF of 23/20,15/69,186/78 is 1/17940.
To find the highest common factor of 23,15,186, we have to find the factors of both numbers and list the highest common factor.
The factors of 23 are 1, 23
The factors of 15 are 1, 3, 5, 15
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186
The HCF of 23,15,186 is 1.
Lets's calculate GCF of 23,15,186
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 23
:1,23
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 186
:1,2,3,6,31,62,93,186
Greatest Common Factor
We found the factors 23,15,186 . The biggest common factor number is the GCF number.
So the greatest common factor 23,15,186 is 1.
Lets's calculate LCM of 20,69,78
2 | 20, 69, 78 |
3 | 10, 69, 39 |
10, 23, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 10 x 23 x 13 = 17940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17940
Therefore, the GCF of Fractions 23/20,15/69,186/78 is 1/17940
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 20,69,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,69,78) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(20,69,78) x common factors =1 x 6 = 6
LCM(20,69,78) = ( 20 × 69 × 78 ) / 6
LCM(20,69,78) = 107640 / 6
LCM(20,69,78) = 17940
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 23,15,186?
The HCF of 23,15,186 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 23/20, 15/69, 186/78?
Answer: GCF of Numerators as per given numbers 23/20, 15/69, 186/78 is
GCF of Numerators i.e. for 23,15,186 is 1
LCM of denominators i.e. for 20,69,78 is 17940.
Thus, GCF of Fractions is 1/17940.Finally, GCF of Fractions for 23/20, 15/69, 186/78 is 1/17940.