In general
An integer $\blue{a}$ is a divisor of an integer $\orange{b}$ if $\orange{b} \div \blue{a}$ results in an integer $\green q$, or in other words $\blue{a} \times \green{q} = \orange{b}$.
The result of the division $\green{q}$ is known as the quotient.

Division with remainder

If we divide a number $\orange{b}$ by a number $\blue{a}$ but $\blue{a}$ is not a divisor of $\orange{b}$, the result is a quotient $\green q$ and a remainder $\purple{r}$, such that

$$\orange{b} = \blue{a} \times \green{q} + \purple{r}$$

The remainder $\purple r$ is a non-negative number smaller than $\blue{a}$.

To find the quotient and remainder when dividing two numbers $\orange{b}$ and $\blue{a}$ where $\blue{a}$ is not a divisor of $\orange{b}$, find the largest number $\green{q}$ such that $\blue{a} \times \green{q}$ is not larger than $\orange{b}$. Then the remainder $\purple{r} = \orange{b} - \blue{a} \times \green{q}$.

Using a calculator, the quotient $\green q$ is found by calculating $\orange{b} \div \blue{a}$ and rounding the answer down, so $\green q$ is the number without the decimals. Then, the remainder $\purple r$ is calculated as $\orange{b} - \blue{a} \times \green{q}$.

Example

The quotient of $\orange{38}$ and $\blue{7}$ is $\green 5$ and the remainder is $\purple 3$.
$$\orange{38} = \blue{7} \times \green{5} + \purple{3}$$

With a calculator we find $\orange{38} \div \blue{7} \approx 5.428571428571429$ hence the quotient is $\green 5$ which leaves the remainder $\orange{38} -\blue{7} \times \green{5} = \purple{3}$.