GCF of 1000/288, 1440/864
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1000/288, 1440/864 i.e 40/864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1000/288, 1440/864.
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 1000/288,1440/864?
Given fractions are 1000/288,1440/864
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 1000/288,1440/864, numerators are 1000,1440
Denominators are 288,864
The GCF of 1000,1440 is 40 .
LCM of 288,864 is 864.
The greatest common factor of 1000/288,1440/864 = [GCF of 1000,1440]/[LCM of 288,864]= 40/864
Therefore, the GCF of 1000/288,1440/864 is 40/864.
To find the highest common factor of 1000,1440, we have to find the factors of both numbers and list the highest common factor.
The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The factors of 1440 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440
The HCF of 1000,1440 is 40.
Lets's calculate GCF of 1000,1440
| 2 | 1000, 1440 |
| 2 | 500, 720 |
| 2 | 250, 360 |
| 5 | 125, 180 |
| 25, 36 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 1000,1440 By Matching Biggest Common Factor Method
Now, list down the factors of 1000
:1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000
Now, list down the factors of 1440
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,32,36,40,45,48,60,72,80,90,96,120,144,160,180,240,288,360,480,720,1440
Greatest Common Factor
We found the factors 1000,1440 . The biggest common factor number is the GCF number.
So the greatest common factor 1000,1440 is 40.
Lets's calculate LCM of 288,864
| 2 | 288, 864 |
| 2 | 144, 432 |
| 2 | 72, 216 |
| 2 | 36, 108 |
| 2 | 18, 54 |
| 3 | 9, 27 |
| 3 | 3, 9 |
| 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 1 x 3 = 864
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/864
Therefore, the GCF of Fractions 1000/288,1440/864 is 40/864
Least Common Multiple of 288,864 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 288,864 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,864) = 288
common factors(in case of two or more numbers have common factors) = 1
GCF(288,864) x common factors =288 x 1 = 288
LCM(288,864) = ( 288 × 864 ) / 288
LCM(288,864) = 248832 / 288
LCM(288,864) = 864
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FAQs on GCF of Fractions of 1000/288, 1440/864
1. What is the HCF of 1000,1440?
The HCF of 1000,1440 is 40
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 1000/288, 1440/864?
Answer: GCF of Numerators as per given numbers 1000/288, 1440/864 is
GCF of Numerators i.e. for 1000,1440 is 40
LCM of denominators i.e. for 288,864 is 864.
Thus, GCF of Fractions is 40/864.Finally, GCF of Fractions for 1000/288, 1440/864 is 40/864.