Use our free GCF of Fractions Calculator tool to compute the GCF of 820/960, 450/205 i.e 10/39360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 820/960, 450/205.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 820/960,450/205
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 820/960,450/205, numerators are 820,450
Denominators are 960,205
The GCF of 820,450 is 10 .
LCM of 960,205 is 39360.
The greatest common factor of 820/960,450/205 = [GCF of 820,450]/[LCM of 960,205]= 10/39360
Therefore, the GCF of 820/960,450/205 is 10/39360.
To find the highest common factor of 820,450, we have to find the factors of both numbers and list the highest common factor.
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The HCF of 820,450 is 10.
Lets's calculate GCF of 820,450
2 | 820, 450 |
5 | 410, 225 |
82, 45 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 820
:1,2,4,5,10,20,41,82,164,205,410,820
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
Greatest Common Factor
We found the factors 820,450 . The biggest common factor number is the GCF number.
So the greatest common factor 820,450 is 10.
Lets's calculate LCM of 960,205
5 | 960, 205 |
192, 41 |
∴ So the LCM of the given numbers is 5 x 192 x 41 = 39360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/39360
Therefore, the GCF of Fractions 820/960,450/205 is 10/39360
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 960,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(960,205) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(960,205) x common factors =5 x 1 = 5
LCM(960,205) = ( 960 × 205 ) / 5
LCM(960,205) = 196800 / 5
LCM(960,205) = 39360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 820,450?
The HCF of 820,450 is 10
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 820/960, 450/205?
Answer: GCF of Numerators as per given numbers 820/960, 450/205 is
GCF of Numerators i.e. for 820,450 is 10
LCM of denominators i.e. for 960,205 is 39360.
Thus, GCF of Fractions is 10/39360.Finally, GCF of Fractions for 820/960, 450/205 is 10/39360.