Exercise · ZW-DIVISIBILITY-008 · ★★☆ Intermediate
Which of the following statements is false?
Choose one option.
Show answer
- A. If \(a\mid bc\), then \(a\mid b\).
Explanation
Counterexample: \(4\mid 2\cdot2\) but \(4\nmid 2\). The other three follow from \(b=ak\).
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-003 If a| b and b| c, what always follows?
- 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-009 How many integers from 1 to 100 are multiples of 3 but not of 4?