Use our free GCF of Fractions Calculator tool to compute the GCF of 33/87, 378/54, 422/324 i.e 1/9396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 33/87, 378/54, 422/324.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 33/87,378/54,422/324
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 33/87,378/54,422/324, numerators are 33,378,422
Denominators are 87,54,324
The GCF of 33,378,422 is 1 .
LCM of 87,54,324 is 9396.
The greatest common factor of 33/87,378/54,422/324 = [GCF of 33,378,422]/[LCM of 87,54,324]= 1/9396
Therefore, the GCF of 33/87,378/54,422/324 is 1/9396.
To find the highest common factor of 33,378,422, we have to find the factors of both numbers and list the highest common factor.
The factors of 33 are 1, 3, 11, 33
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 422 are 1, 2, 211, 422
The HCF of 33,378,422 is 1.
Lets's calculate GCF of 33,378,422
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 33
:1,3,11,33
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 422
:1,2,211,422
Greatest Common Factor
We found the factors 33,378,422 . The biggest common factor number is the GCF number.
So the greatest common factor 33,378,422 is 1.
Lets's calculate LCM of 87,54,324
2 | 87, 54, 324 |
3 | 87, 27, 162 |
3 | 29, 9, 54 |
3 | 29, 3, 18 |
29, 1, 6 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 29 x 1 x 6 = 9396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9396
Therefore, the GCF of Fractions 33/87,378/54,422/324 is 1/9396
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 87,54,324 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,54,324) = 3
common factors(in case of two or more numbers have common factors) = 54
GCF(87,54,324) x common factors =3 x 54 = 162
LCM(87,54,324) = ( 87 × 54 × 324 ) / 162
LCM(87,54,324) = 1522152 / 162
LCM(87,54,324) = 9396
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 33,378,422?
The HCF of 33,378,422 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 33/87, 378/54, 422/324?
Answer: GCF of Numerators as per given numbers 33/87, 378/54, 422/324 is
GCF of Numerators i.e. for 33,378,422 is 1
LCM of denominators i.e. for 87,54,324 is 9396.
Thus, GCF of Fractions is 1/9396.Finally, GCF of Fractions for 33/87, 378/54, 422/324 is 1/9396.