Use our free GCF of Fractions Calculator tool to compute the GCF of 410/367, 960/326 i.e 10/119642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/367, 960/326.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 410/367,960/326
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 410/367,960/326, numerators are 410,960
Denominators are 367,326
The GCF of 410,960 is 10 .
LCM of 367,326 is 119642.
The greatest common factor of 410/367,960/326 = [GCF of 410,960]/[LCM of 367,326]= 10/119642
Therefore, the GCF of 410/367,960/326 is 10/119642.
To find the highest common factor of 410,960, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 410,960 is 10.
Lets's calculate GCF of 410,960
2 | 410, 960 |
5 | 205, 480 |
41, 96 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 410,960 . The biggest common factor number is the GCF number.
So the greatest common factor 410,960 is 10.
Lets's calculate LCM of 367,326
Given numbers has no common factors except 1. So, there LCM is their product i.e 119642
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/119642
Therefore, the GCF of Fractions 410/367,960/326 is 10/119642
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 367,326 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(367,326) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(367,326) x common factors =1 x 1 = 1
LCM(367,326) = ( 367 × 326 ) / 1
LCM(367,326) = 119642 / 1
LCM(367,326) = 119642
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 410,960?
The HCF of 410,960 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 410/367, 960/326?
Answer: GCF of Numerators as per given numbers 410/367, 960/326 is
GCF of Numerators i.e. for 410,960 is 10
LCM of denominators i.e. for 367,326 is 119642.
Thus, GCF of Fractions is 10/119642.Finally, GCF of Fractions for 410/367, 960/326 is 10/119642.