Use our free GCF of Fractions Calculator tool to compute the GCF of 660/993, 168/465 i.e 12/153915 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/993, 168/465.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 660/993,168/465
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 660/993,168/465, numerators are 660,168
Denominators are 993,465
The GCF of 660,168 is 12 .
LCM of 993,465 is 153915.
The greatest common factor of 660/993,168/465 = [GCF of 660,168]/[LCM of 993,465]= 12/153915
Therefore, the GCF of 660/993,168/465 is 12/153915.
To find the highest common factor of 660,168, we have to find the factors of both numbers and list the highest common factor.
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The HCF of 660,168 is 12.
Lets's calculate GCF of 660,168
2 | 660, 168 |
2 | 330, 84 |
3 | 165, 42 |
55, 14 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Greatest Common Factor
We found the factors 660,168 . The biggest common factor number is the GCF number.
So the greatest common factor 660,168 is 12.
Lets's calculate LCM of 993,465
3 | 993, 465 |
331, 155 |
∴ So the LCM of the given numbers is 3 x 331 x 155 = 153915
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/153915
Therefore, the GCF of Fractions 660/993,168/465 is 12/153915
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 993,465 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(993,465) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(993,465) x common factors =3 x 1 = 3
LCM(993,465) = ( 993 × 465 ) / 3
LCM(993,465) = 461745 / 3
LCM(993,465) = 153915
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 660,168?
The HCF of 660,168 is 12
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 660/993, 168/465?
Answer: GCF of Numerators as per given numbers 660/993, 168/465 is
GCF of Numerators i.e. for 660,168 is 12
LCM of denominators i.e. for 993,465 is 153915.
Thus, GCF of Fractions is 12/153915.Finally, GCF of Fractions for 660/993, 168/465 is 12/153915.