The problem asks, "How many integers between 1 and 100 (inclusive) are divisible by 5?"

To solve this:

1. The integers divisible by 5 are of the form $5n$, where $n$ is an integer.
2. We need to find all such integers from 1 to 100.

The smallest number divisible by 5 in this range is $5 \times 1 = 5$, and the largest number divisible by 5 is $5 \times 20 = 100$.

Thus, the integers divisible by 5 are $5, 10, 15, \dots, 100$.

Now, to find how many such numbers exist:

• This is an arithmetic sequence where the first term $a = 5$, the common difference $d = 5$, and the last term $l = 100$.
• The number of terms in this sequence is given by the formula: $n = \frac{l - a}{d} + 1$ Substituting the values: $n = \frac{100 - 5}{5} + 1 = \frac{95}{5} + 1 = 19 + 1 = 20$

Thus, there are 20 integers between 1 and 100 that are divisible by 5. The correct answer is c. 20.

Would you like further clarification or details?

Here are 5 related questions to explore:

1. What are the integers between 1 and 100 divisible by 3?
2. How many integers between 1 and 200 are divisible by 7?
3. How many prime numbers are there between 1 and 100?
4. How many integers between 50 and 150 are divisible by 6?
5. How can you find the number of integers divisible by a given number within any range?

Tip: When dealing with divisibility problems, listing the first and last terms helps set up a clear arithmetic sequence to count the numbers efficiently.