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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