Exercise · ZW-DIVISIBILITY-003 · ★☆☆ Basic
If \(a\mid b\) and \(b\mid c\), what always follows?
Choose one option.
Show answer
- A. \(a\mid c\)
Explanation
If \(b=ak\) and \(c=bj\), then \(c=a(kj)\), so \(a\mid c\). Divisibility is transitive but not symmetric.
Review the concept: Divisibility
An integer \(a\neq0\) divides an integer \(b\), written \(a\mid b\), when \(b\) is an integer multiple of \(a\).
\[a\mid b\iff b=ak\ \text{for some } k\in\mathbb{Z}\]
More practice problems: divisibility
- ZW-DIVISIBILITY-001 Which of the following statements is true?
- ZW-DIVISIBILITY-002 How many positive multiples of 6 lie between 1 and 100?
- ZW-DIVISIBILITY-004 Which of these numbers is divisible by 12?
- ZW-DIVISIBILITY-005 How many positive divisors does 36 have?
- ZW-DIVISIBILITY-006 How many positive integers n satisfy n| n+12?
- ZW-DIVISIBILITY-007 What is the largest positive integer a that divides both 24 and 36?
- ZW-DIVISIBILITY-008 Which of the following statements is false?
- ZW-DIVISIBILITY-009 How many integers from 1 to 100 are multiples of 3 but not of 4?