Use our free GCF of Fractions Calculator tool to compute the GCF of 450/204, 664/322 i.e 2/32844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/204, 664/322.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 450/204,664/322
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 450/204,664/322, numerators are 450,664
Denominators are 204,322
The GCF of 450,664 is 2 .
LCM of 204,322 is 32844.
The greatest common factor of 450/204,664/322 = [GCF of 450,664]/[LCM of 204,322]= 2/32844
Therefore, the GCF of 450/204,664/322 is 2/32844.
To find the highest common factor of 450,664, we have to find the factors of both numbers and list the highest common factor.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The factors of 664 are 1, 2, 4, 8, 83, 166, 332, 664
The HCF of 450,664 is 2.
Lets's calculate GCF of 450,664
2 | 450, 664 |
225, 332 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
Now, list down the factors of 664
:1,2,4,8,83,166,332,664
Greatest Common Factor
We found the factors 450,664 . The biggest common factor number is the GCF number.
So the greatest common factor 450,664 is 2.
Lets's calculate LCM of 204,322
2 | 204, 322 |
102, 161 |
∴ So the LCM of the given numbers is 2 x 102 x 161 = 32844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/32844
Therefore, the GCF of Fractions 450/204,664/322 is 2/32844
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 204,322 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,322) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(204,322) x common factors =2 x 1 = 2
LCM(204,322) = ( 204 × 322 ) / 2
LCM(204,322) = 65688 / 2
LCM(204,322) = 32844
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 450,664?
The HCF of 450,664 is 2
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 450/204, 664/322?
Answer: GCF of Numerators as per given numbers 450/204, 664/322 is
GCF of Numerators i.e. for 450,664 is 2
LCM of denominators i.e. for 204,322 is 32844.
Thus, GCF of Fractions is 2/32844.Finally, GCF of Fractions for 450/204, 664/322 is 2/32844.