Use our free GCF of Fractions Calculator tool to compute the GCF of 87/168, 45/5826 i.e 3/163128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/168, 45/5826.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 87/168,45/5826
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 87/168,45/5826, numerators are 87,45
Denominators are 168,5826
The GCF of 87,45 is 3 .
LCM of 168,5826 is 163128.
The greatest common factor of 87/168,45/5826 = [GCF of 87,45]/[LCM of 168,5826]= 3/163128
Therefore, the GCF of 87/168,45/5826 is 3/163128.
To find the highest common factor of 87,45, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 45 are 1, 3, 5, 9, 15, 45
The HCF of 87,45 is 3.
Lets's calculate GCF of 87,45
3 | 87, 45 |
29, 15 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 45
:1,3,5,9,15,45
Greatest Common Factor
We found the factors 87,45 . The biggest common factor number is the GCF number.
So the greatest common factor 87,45 is 3.
Lets's calculate LCM of 168,5826
2 | 168, 5826 |
3 | 84, 2913 |
28, 971 |
∴ So the LCM of the given numbers is 2 x 3 x 28 x 971 = 163128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/163128
Therefore, the GCF of Fractions 87/168,45/5826 is 3/163128
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 168,5826 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(168,5826) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(168,5826) x common factors =6 x 1 = 6
LCM(168,5826) = ( 168 × 5826 ) / 6
LCM(168,5826) = 978768 / 6
LCM(168,5826) = 163128
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 87,45?
The HCF of 87,45 is 3
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 87/168, 45/5826?
Answer: GCF of Numerators as per given numbers 87/168, 45/5826 is
GCF of Numerators i.e. for 87,45 is 3
LCM of denominators i.e. for 168,5826 is 163128.
Thus, GCF of Fractions is 3/163128.Finally, GCF of Fractions for 87/168, 45/5826 is 3/163128.