Counting Numbers Divisible by 5 Between 1 and 100: A Comprehensive Guide
Understanding the concept of numbers divisible by 5 can be a fascinating topic in basic mathematics. In this article, we will explore how to count the numbers between 1 and 100 that are divisible by 5 using various methods, including listing, formulas, and logical reasoning. This guide aims to provide a clear and intuitive understanding of this mathematical concept.
Listing Multiples of 5
The simplest way to ascertain how many numbers are divisible by 5 between 1 and 100 is by listing them explicitly:
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100By counting each of these numbers, we find that there are 20 numbers between 1 and 100 that are divisible by 5.
Using the Arithmetic Sequence Formula
Another method to determine the number of multiples of 5 between 1 and 100 is through the formula for an arithmetic sequence. The formula for the number of terms in an arithmetic sequence is:
n (last term - first term) / common difference 1
Here:
The first multiple of 5 in this range is 5. The last multiple of 5 is 100. The common difference (or the increment) is 5.Substituting these values into the formula:
First term 5
Last term 100
Common difference 5
n (100 - 5) / 5 1
95 / 5 1
19 1
20
Therefore, using the arithmetic sequence formula, we also find that there are 20 multiples of 5 between 1 and 100.
Alternatives and Considerations
It is important to note that if 100 is not included, the answer would be 19. This is because 100 itself is a multiple of 5:
100 / 5 20 (including 100)
100 / 5 19 (excluding 100)
This is a straightforward way to determine the exact number of multiples of 5 within any specified range.
Conclusion
Counting numbers divisible by 5 is a fundamental mathematical skill that can be achieved through various methods. Whether you choose to list the multiples or use the arithmetic sequence formula, the result remains consistent: there are 20 multiples of 5 between 1 and 100. This guide aims to provide a comprehensive understanding of the concept, making it accessible and easy to grasp.