GCF of 9900/585, 1509/297
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9900/585, 1509/297 i.e 3/19305 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9900/585, 1509/297.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 9900/585,1509/297?
Given fractions are 9900/585,1509/297
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 9900/585,1509/297, numerators are 9900,1509
Denominators are 585,297
The GCF of 9900,1509 is 3 .
LCM of 585,297 is 19305.
The greatest common factor of 9900/585,1509/297 = [GCF of 9900,1509]/[LCM of 585,297]= 3/19305
Therefore, the GCF of 9900/585,1509/297 is 3/19305.
To find the highest common factor of 9900,1509, we have to find the factors of both numbers and list the highest common factor.
The factors of 9900 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900
The factors of 1509 are 1, 3, 503, 1509
The HCF of 9900,1509 is 3.
Lets's calculate GCF of 9900,1509
| 3 | 9900, 1509 |
| 3300, 503 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9900,1509 By Matching Biggest Common Factor Method
Now, list down the factors of 9900
:1,2,3,4,5,6,9,10,11,12,15,18,20,22,25,30,33,36,44,45,50,55,60,66,75,90,99,100,110,132,150,165,180,198,220,225,275,300,330,396,450,495,550,660,825,900,990,1100,1650,1980,2475,3300,4950,9900
Now, list down the factors of 1509
:1,3,503,1509
Greatest Common Factor
We found the factors 9900,1509 . The biggest common factor number is the GCF number.
So the greatest common factor 9900,1509 is 3.
Lets's calculate LCM of 585,297
| 3 | 585, 297 |
| 3 | 195, 99 |
| 65, 33 |
∴ So the LCM of the given numbers is 3 x 3 x 65 x 33 = 19305
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/19305
Therefore, the GCF of Fractions 9900/585,1509/297 is 3/19305
Least Common Multiple of 585,297 with GCF Formula
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 585,297 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,297) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(585,297) x common factors =9 x 1 = 9
LCM(585,297) = ( 585 × 297 ) / 9
LCM(585,297) = 173745 / 9
LCM(585,297) = 19305
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FAQs on GCF of Fractions of 9900/585, 1509/297
1. What is the HCF of 9900,1509?
The HCF of 9900,1509 is 3
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 9900/585, 1509/297?
Answer: GCF of Numerators as per given numbers 9900/585, 1509/297 is
GCF of Numerators i.e. for 9900,1509 is 3
LCM of denominators i.e. for 585,297 is 19305.
Thus, GCF of Fractions is 3/19305.Finally, GCF of Fractions for 9900/585, 1509/297 is 3/19305.