adkikani wrote:

Bunuel niks18 chetan2u KarishmaB GMATPrepNow pushpitkc generis**Quote:**

If \(@x\) is the number of distinct positive divisors of \(x\), what is the value of \(@(@90)\)?

**Quote:**

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and \(n\) itself.

Correct, but is not question asking us the distinct number of factors and not a TOTAL number of factors?

90 can be factorized in terms of primes as \(3^2\) , 2 and 5

UNIQUE Factors will be only 2,3 and 5. Am I correct?

How about 6? Isn't that a unique factor too? What about 15? etc

As Bunuel said, no of factors is the same as unique factors. Note that we do not count 3 twice

\(90 = 2*3^2 * 5\)

Distinct Prime factors are 2, 3 and 5.

All unique factors are

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Total 12 factors

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Karishma

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