3 steps to find out the number of natural numbers that are divisible by certain numbers

“How many natural numbers between 200 and 500 are divisible by 2,3,4,5 and 6?”

This is an interesting question that I found online when I did a google search for math olympiad questions. What I found particularly interesting is that you can approach this question using ‘guess and check’ or an understanding of the properties of numbers. Of course, these are not the only ways to solve this question and our readers may have more approaches to this sum.

In this article, I will demonstrate an approach to this question based on understanding the divisibility of the numbers 2, 3, 4, 5, and 6. I find this approach to be a very neat way to solve this question, and students can figure this out. ask in less than 2 minutes.

But first, what are the natural numbers?

What are the natural numbers?
According to Wolfram’s website, natural numbers refer to a set of positive integers like 1,2,3… or to a set of non-negative integers 0,1,2,3… or simply, they are Numbers used to tell. There is also a debate about whether to include the number 0 in the category of natural numbers, but that is not the subject of this article.

Getting closer
So how do you approach this question?

You could try dividing the range of numbers by 2, 3, 4, 5, and 6, but this approach would be too tedious.

Step 1: simplify the problem through observation

A simple method might be to observe that the number 2 is a factor of both 4 (2 x 2) and 6 (3 x 2). If the numbers can be divided by 2, they can also be divided by 4 and 6, so we only need to focus on the numbers 2, 2, 3, and 5.

Step 2: Multiply the numbers

Multiplying the numbers, 2x2x3x5 gives us 60. So if any number in the range of 200 to 500 can be divided by 60, then that’s the natural number we’re looking for.

Step 3: Conclusion
So the natural numbers are 240, 300,360, 420 and 480. A total of 5 natural numbers.
I hope this approach is a quick and easy way to quickly figure out the number of whole numbers that are divisible by 2,3,4,5 and 6.

Using the example above, try to generalize the approach to similar questions.