GCF of 500/250, 900/585
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 500/250, 900/585 i.e 100/29250 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/250, 900/585.
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 500/250,900/585?
Given fractions are 500/250,900/585
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 500/250,900/585, numerators are 500,900
Denominators are 250,585
The GCF of 500,900 is 100 .
LCM of 250,585 is 29250.
The greatest common factor of 500/250,900/585 = [GCF of 500,900]/[LCM of 250,585]= 100/29250
Therefore, the GCF of 500/250,900/585 is 100/29250.
To find the highest common factor of 500,900, we have to find the factors of both numbers and list the highest common factor.
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
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 HCF of 500,900 is 100.
Lets's calculate GCF of 500,900
| 2 | 500, 900 |
| 2 | 250, 450 |
| 5 | 125, 225 |
| 5 | 25, 45 |
| 5, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100
Greatest Common Factor of 500,900 By Matching Biggest Common Factor Method
Now, list down the factors of 500
:1,2,4,5,10,20,25,50,100,125,250,500
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
Greatest Common Factor
We found the factors 500,900 . The biggest common factor number is the GCF number.
So the greatest common factor 500,900 is 100.
Lets's calculate LCM of 250,585
| 5 | 250, 585 |
| 50, 117 |
∴ So the LCM of the given numbers is 5 x 50 x 117 = 29250
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/29250
Therefore, the GCF of Fractions 500/250,900/585 is 100/29250
Least Common Multiple of 250,585 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 250,585 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(250,585) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(250,585) x common factors =5 x 1 = 5
LCM(250,585) = ( 250 × 585 ) / 5
LCM(250,585) = 146250 / 5
LCM(250,585) = 29250
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 500/250, 900/585
1. What is the HCF of 500,900?
The HCF of 500,900 is 100
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 500/250, 900/585?
Answer: GCF of Numerators as per given numbers 500/250, 900/585 is
GCF of Numerators i.e. for 500,900 is 100
LCM of denominators i.e. for 250,585 is 29250.
Thus, GCF of Fractions is 100/29250.Finally, GCF of Fractions for 500/250, 900/585 is 100/29250.