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How many positive divisors does $2000$ have?

$A)12$             $B)20$                    $C)30$               $D)15$

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Option B

2000=2^4*5^3

No of divisor =(4+1)*(3+1)=5*4=20

For any number n total no of divisor is given by

n=p1^a1*p2^a2...

Where p1,p2 are prime numbers

Then no of divisor =(a1+1)*(a2+1)...

This can be explained using counting...We take prime so it cannot be further factorised so take this que as example

2000=2^4*5^3

In this lets take 5^3

We can take 3 5 or 2 5 or 1 5 or 0 5 so 4 ways similarly for 2^4 5 ways

Therefore total ways=5*4=20
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