Use our free GCF of Fractions Calculator tool to compute the GCF of 900/910, 540/585 i.e 180/8190 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/910, 540/585.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 900/910,540/585
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 900/910,540/585, numerators are 900,540
Denominators are 910,585
The GCF of 900,540 is 180 .
LCM of 910,585 is 8190.
The greatest common factor of 900/910,540/585 = [GCF of 900,540]/[LCM of 910,585]= 180/8190
Therefore, the GCF of 900/910,540/585 is 180/8190.
To find the highest common factor of 900,540, we have to find the factors of both numbers and list the highest common factor.
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 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The HCF of 900,540 is 180.
Lets's calculate GCF of 900,540
2 | 900, 540 |
2 | 450, 270 |
3 | 225, 135 |
3 | 75, 45 |
5 | 25, 15 |
5, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 x 5 = 180
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 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Greatest Common Factor
We found the factors 900,540 . The biggest common factor number is the GCF number.
So the greatest common factor 900,540 is 180.
Lets's calculate LCM of 910,585
5 | 910, 585 |
13 | 182, 117 |
14, 9 |
∴ So the LCM of the given numbers is 5 x 13 x 14 x 9 = 8190
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 180/8190
Therefore, the GCF of Fractions 900/910,540/585 is 180/8190
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 910,585 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(910,585) = 65
common factors(in case of two or more numbers have common factors) = 1
GCF(910,585) x common factors =65 x 1 = 65
LCM(910,585) = ( 910 × 585 ) / 65
LCM(910,585) = 532350 / 65
LCM(910,585) = 8190
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 900,540?
The HCF of 900,540 is 180
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 900/910, 540/585?
Answer: GCF of Numerators as per given numbers 900/910, 540/585 is
GCF of Numerators i.e. for 900,540 is 180
LCM of denominators i.e. for 910,585 is 8190.
Thus, GCF of Fractions is 180/8190.Finally, GCF of Fractions for 900/910, 540/585 is 180/8190.