Question

Which one of the given numbers is completely divisible by $45$?

• A. $202860$
• B. $202560$
• C. $213860$
• D. None of these

Answer 1

Answer: (A)

$202860$

$\Rightarrow$ We know that $45=9\times 5$

$\Rightarrow$ If a number is divisible by $5$ and $9$, the number will be divisible by their product $45$ also.

$\Rightarrow$ If a number is not divisible by $5$ or $9$, it is not divisible by $45$.

$\Rightarrow$ Divisibility rule of $5$ : If it ends with a $5$ or a $0$.

$\Rightarrow$ Divisibility rule of $9$ : If the sum of the digits are a multiple of $9$.

$\Rightarrow$ $202860$ is divisible by $5$ and $9;$ So, $202860$ is divisible by $45$

$\Rightarrow$ $202560$ is divisible by $5$ but not divisible by $9;$ So, $202560$ is not divisible by $45$.

$\Rightarrow$ $213860$ is divisible by $5$ but not divisible by $9;$ So, $213860$ is not divisible by $45$