Question

How many positive integers between $1000$ and $9999$ inclusive are divisible by $5$ and $7$?

Answer 1

Finding the number of positive integers between $1000$ and $9999$ inclusive that are divisible by $5$ and $7$.

The total number of positive integers between $1000$ and $9999$ inclusive are $9999-999=9000$.

The total number of positive integers between $1000$ and $9999$ inclusive that are divisible by $5$ and $7$ can be calculated by dividing the total number of positive integers by the $\mathrm{GCF}$ of $5$ and $7$.

$\mathrm{GCF}$ of $5$ and $7$$=35$.

Number of positive integers$\begin{array}{rcl}& =& \frac{9000}{35}\end{array}$

$\begin{array}{rcl}& =& 257.14\\ & \approx & 257\end{array}$

Hence, there are $257$ positive integers between $1000$ and $9999$ inclusive that are divisible by $5$ and $7$.