Use our free GCF of Fractions Calculator tool to compute the GCF of 660/900, 308/453 i.e 44/135900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/900, 308/453.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 660/900,308/453
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 660/900,308/453, numerators are 660,308
Denominators are 900,453
The GCF of 660,308 is 44 .
LCM of 900,453 is 135900.
The greatest common factor of 660/900,308/453 = [GCF of 660,308]/[LCM of 900,453]= 44/135900
Therefore, the GCF of 660/900,308/453 is 44/135900.
To find the highest common factor of 660,308, 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 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The HCF of 660,308 is 44.
Lets's calculate GCF of 660,308
2 | 660, 308 |
2 | 330, 154 |
11 | 165, 77 |
15, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 11 = 44
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 308
:1,2,4,7,11,14,22,28,44,77,154,308
Greatest Common Factor
We found the factors 660,308 . The biggest common factor number is the GCF number.
So the greatest common factor 660,308 is 44.
Lets's calculate LCM of 900,453
3 | 900, 453 |
300, 151 |
∴ So the LCM of the given numbers is 3 x 300 x 151 = 135900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 44/135900
Therefore, the GCF of Fractions 660/900,308/453 is 44/135900
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 900,453 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(900,453) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(900,453) x common factors =3 x 1 = 3
LCM(900,453) = ( 900 × 453 ) / 3
LCM(900,453) = 407700 / 3
LCM(900,453) = 135900
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 660,308?
The HCF of 660,308 is 44
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 660/900, 308/453?
Answer: GCF of Numerators as per given numbers 660/900, 308/453 is
GCF of Numerators i.e. for 660,308 is 44
LCM of denominators i.e. for 900,453 is 135900.
Thus, GCF of Fractions is 44/135900.Finally, GCF of Fractions for 660/900, 308/453 is 44/135900.