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Arithmetic Foundations Mastery Hub: The Industry Foundation

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Q1Domain Verified
s for "Arithmetic Foundations Mastery Hub: The Industry Foundation," based on the topic "{The Complete Number System & Divisibility Course 2026: From Zero to Expert!}": Question: Consider the set of integers $Z$. If $a, b \in Z$, which of the following properties is NOT a fundamental characteristic of the divisibility relation on $Z$?
Reflexivity: For any $a \in Z$, $a | a$.
Transitivity: For any $a, b, c \in Z$, if $a | b$ and $b | c$, then $a | c$.
Antisymmetry: For any $a, b \in Z$, if $a | b$ and $b | a$, then $a = b$ or $a = -b$.
Symmetry: For any $a, b \in Z$, if $a | b$, then $b | a$.
Q2Domain Verified
Let $n$ be a positive integer. If the prime factorization of $n$ is given by $n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k}$, where $p_i$ are distinct prime numbers and $a_i \ge 1$, what is the total number of positive divisors of $n$?
$2^k$
$p_1^{a_1+1} p_2^{a_2+1} \cdots p_k^{a_k+1}$
$a_1 + a_2 + \cdots + a_k$
$(a_1 + 1)(a_2 + 1) \cdots (a_k + 1)$
Q3Domain Verified
An integer $N$ is divisible by 9 if and only if the sum of its digits is divisible by 9. If $N = 78A3B$, where $A$ and $B$ are digits, and $N$ is divisible by both 5 and 9, what is the value of $A \times B$?
{ "text": "", "is_correct": true }
27
36
18

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