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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.

How many integers between 1 and 100 (inclusive) are divisible by 5?

Find out how many integers between 1 and 100 are divisible by 5 using arithmetic sequence formulas. This solution breaks down the method to count integers divisible by a given number, perfect for students in Grades 6-8.

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