Question

Which of the following can not be the possible values of $a$ if $45\equiv 0\text{(mod a)}?$

• A. 9
• B. 5
• C. 3
• D. 14

Answer 1

The correct option is D 14

Two integers $a$ and $b$ are congruent modulo $n,$ if they differ by an integer multiple of $n.$
This can be represented as $a\equiv b\left(modn\right),$which means that $a-b$ is divisible by $n.$

Given: $45\equiv 0\text{(mod a)}$
This means 45 is divisible by a.
The factors of 45 = 1, 3, 5, 9, 15, 45.
Therefore, the possible values of a = 1, 3, 5, 9, 15, 45.