The symbol is just a symbol, it means nothing. In the question it denotes some function relationship.

The question defines "@x" as the number of distinct positive divisors of x. Say @6=4, as 6 have 4 distinct positive divisors: 1, 2, 3, 6.

@@90 -->

90=2*3^2*5 the number of distinct factors (divisors) of 90 can be found by the formula: (1+1)(2+1)(1+1)=12. So @90=12 --> @12=? 12=2^2*3, again the number of distinct factors (divisors) of 12 can be found by the formula: (2+1)(1+1)=6.

Answer: D (6)

General rule:

Finding the Number of Factors of an IntegerFirst 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.

Example: Finding the number of all factors of 450:

450=2^1*3^2*5^2Total number of factors of 450 including 1 and 450 itself is

(1+1)*(2+1)*(2+1)=2*3*3=18 factors.

This question is about the number properties. You can check the Number Theory chapter in MathBook (link below), sorry it's not finished yet.

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