GCF of 2000/405, 8872/2707
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2000/405, 8872/2707 i.e 8/1096335 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2000/405, 8872/2707.
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 2000/405,8872/2707?
Given fractions are 2000/405,8872/2707
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 2000/405,8872/2707, numerators are 2000,8872
Denominators are 405,2707
The GCF of 2000,8872 is 8 .
LCM of 405,2707 is 1096335.
The greatest common factor of 2000/405,8872/2707 = [GCF of 2000,8872]/[LCM of 405,2707]= 8/1096335
Therefore, the GCF of 2000/405,8872/2707 is 8/1096335.
To find the highest common factor of 2000,8872, we have to find the factors of both numbers and list the highest common factor.
The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000
The factors of 8872 are 1, 2, 4, 8, 1109, 2218, 4436, 8872
The HCF of 2000,8872 is 8.
Lets's calculate GCF of 2000,8872
| 2 | 2000, 8872 |
| 2 | 1000, 4436 |
| 2 | 500, 2218 |
| 250, 1109 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 2000,8872 By Matching Biggest Common Factor Method
Now, list down the factors of 2000
:1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000
Now, list down the factors of 8872
:1,2,4,8,1109,2218,4436,8872
Greatest Common Factor
We found the factors 2000,8872 . The biggest common factor number is the GCF number.
So the greatest common factor 2000,8872 is 8.
Lets's calculate LCM of 405,2707
Given numbers has no common factors except 1. So, there LCM is their product i.e 1096335
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/1096335
Therefore, the GCF of Fractions 2000/405,8872/2707 is 8/1096335
Least Common Multiple of 405,2707 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 405,2707 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,2707) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(405,2707) x common factors =1 x 1 = 1
LCM(405,2707) = ( 405 × 2707 ) / 1
LCM(405,2707) = 1096335 / 1
LCM(405,2707) = 1096335
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FAQs on GCF of Fractions of 2000/405, 8872/2707
1. What is the HCF of 2000,8872?
The HCF of 2000,8872 is 8
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 2000/405, 8872/2707?
Answer: GCF of Numerators as per given numbers 2000/405, 8872/2707 is
GCF of Numerators i.e. for 2000,8872 is 8
LCM of denominators i.e. for 405,2707 is 1096335.
Thus, GCF of Fractions is 8/1096335.Finally, GCF of Fractions for 2000/405, 8872/2707 is 8/1096335.