Use our free GCF of Fractions Calculator tool to compute the GCF of 90/823, 70/686, 405/942 i.e 5/265916238 easily. The following is the detailed procedure to determine the greatest common factor of fractions 90/823, 70/686, 405/942.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 90/823,70/686,405/942
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 90/823,70/686,405/942, numerators are 90,70,405
Denominators are 823,686,942
The GCF of 90,70,405 is 5 .
LCM of 823,686,942 is 265916238.
The greatest common factor of 90/823,70/686,405/942 = [GCF of 90,70,405]/[LCM of 823,686,942]= 5/265916238
Therefore, the GCF of 90/823,70/686,405/942 is 5/265916238.
To find the highest common factor of 90,70,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 90,70,405 is 5.
Lets's calculate GCF of 90,70,405
5 | 90, 70, 405 |
18, 14, 81 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 90,70,405 . The biggest common factor number is the GCF number.
So the greatest common factor 90,70,405 is 5.
Lets's calculate LCM of 823,686,942
2 | 823, 686, 942 |
823, 343, 471 |
∴ So the LCM of the given numbers is 2 x 823 x 343 x 471 = 265916238
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/265916238
Therefore, the GCF of Fractions 90/823,70/686,405/942 is 5/265916238
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 823,686,942 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(823,686,942) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(823,686,942) x common factors =1 x 2 = 2
LCM(823,686,942) = ( 823 × 686 × 942 ) / 2
LCM(823,686,942) = 531832476 / 2
LCM(823,686,942) = 265916238
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 90,70,405?
The HCF of 90,70,405 is 5
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 90/823, 70/686, 405/942?
Answer: GCF of Numerators as per given numbers 90/823, 70/686, 405/942 is
GCF of Numerators i.e. for 90,70,405 is 5
LCM of denominators i.e. for 823,686,942 is 265916238.
Thus, GCF of Fractions is 5/265916238.Finally, GCF of Fractions for 90/823, 70/686, 405/942 is 5/265916238.