Use our free GCF of Fractions Calculator tool to compute the GCF of 960/984, 465/609 i.e 15/199752 easily. The following is the detailed procedure to determine the greatest common factor of fractions 960/984, 465/609.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 960/984,465/609
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 960/984,465/609, numerators are 960,465
Denominators are 984,609
The GCF of 960,465 is 15 .
LCM of 984,609 is 199752.
The greatest common factor of 960/984,465/609 = [GCF of 960,465]/[LCM of 984,609]= 15/199752
Therefore, the GCF of 960/984,465/609 is 15/199752.
To find the highest common factor of 960,465, we have to find the factors of both numbers and list the highest common factor.
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 factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The HCF of 960,465 is 15.
Lets's calculate GCF of 960,465
3 | 960, 465 |
5 | 320, 155 |
64, 31 |
∴ So the GCF of the given numbers is 3 x 5 = 15
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
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Greatest Common Factor
We found the factors 960,465 . The biggest common factor number is the GCF number.
So the greatest common factor 960,465 is 15.
Lets's calculate LCM of 984,609
3 | 984, 609 |
328, 203 |
∴ So the LCM of the given numbers is 3 x 328 x 203 = 199752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/199752
Therefore, the GCF of Fractions 960/984,465/609 is 15/199752
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 984,609 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(984,609) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(984,609) x common factors =3 x 1 = 3
LCM(984,609) = ( 984 × 609 ) / 3
LCM(984,609) = 599256 / 3
LCM(984,609) = 199752
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 960,465?
The HCF of 960,465 is 15
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 960/984, 465/609?
Answer: GCF of Numerators as per given numbers 960/984, 465/609 is
GCF of Numerators i.e. for 960,465 is 15
LCM of denominators i.e. for 984,609 is 199752.
Thus, GCF of Fractions is 15/199752.Finally, GCF of Fractions for 960/984, 465/609 is 15/199752.