2017 · Q21
a, b, c, d are non-zero integers such that (ab) divides (cd). If a and c are coprime, then which one of the following is correct ?
Elementary MathematicsNumber System
- Aa is a factor of c
- Ba is a factor of b
- Ca is a factor of d
- Dd is a factor of a
Explanation
Since ab divides cd and gcd(a,c) = 1, none of a's prime factors can divide c. All of a's prime factors (counting multiplicity) must therefore divide d, i.e. a | d. Hence option (C) 'a is a factor of d'. (Trap: a and c being coprime rules out option (A), not (C).)