GCF of 20/30, 900/23, 990/561
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 20/30, 900/23, 990/561 i.e 10/129030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/30, 900/23, 990/561.
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 20/30,900/23,990/561?
Given fractions are 20/30,900/23,990/561
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 20/30,900/23,990/561, numerators are 20,900,990
Denominators are 30,23,561
The GCF of 20,900,990 is 10 .
LCM of 30,23,561 is 129030.
The greatest common factor of 20/30,900/23,990/561 = [GCF of 20,900,990]/[LCM of 30,23,561]= 10/129030
Therefore, the GCF of 20/30,900/23,990/561 is 10/129030.
To find the highest common factor of 20,900,990, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
The HCF of 20,900,990 is 10.
Lets's calculate GCF of 20,900,990
| 2 | 20, 900, 990 |
| 5 | 10, 450, 495 |
| 2, 90, 99 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 20,900,990 By Matching Biggest Common Factor Method
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Now, list down the factors of 990
:1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990
Greatest Common Factor
We found the factors 20,900,990 . The biggest common factor number is the GCF number.
So the greatest common factor 20,900,990 is 10.
Lets's calculate LCM of 30,23,561
| 3 | 30, 23, 561 |
| 10, 23, 187 |
∴ So the LCM of the given numbers is 3 x 10 x 23 x 187 = 129030
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/129030
Therefore, the GCF of Fractions 20/30,900/23,990/561 is 10/129030
Least Common Multiple of 30,23,561 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 30,23,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,23,561) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(30,23,561) x common factors =1 x 3 = 3
LCM(30,23,561) = ( 30 × 23 × 561 ) / 3
LCM(30,23,561) = 387090 / 3
LCM(30,23,561) = 129030
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 20/30, 900/23, 990/561
1. What is the HCF of 20,900,990?
The HCF of 20,900,990 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 20/30, 900/23, 990/561?
Answer: GCF of Numerators as per given numbers 20/30, 900/23, 990/561 is
GCF of Numerators i.e. for 20,900,990 is 10
LCM of denominators i.e. for 30,23,561 is 129030.
Thus, GCF of Fractions is 10/129030.Finally, GCF of Fractions for 20/30, 900/23, 990/561 is 10/129030.