Prime Numbers, HCF & LCM: Determining A Prime Number

Introduction

Welcome back to another Secondary 1 Math blog post.

Today, we will be talking about prime numbers — what they are, and how to determine if a certain number is a prime number.

If you are a Secondary 1 student learning this for the first time, keep reading because I will teach you a quick method you can use.

Let’s Take A Look At This Question

The question wants us to determine if 113 is a prime number.

🏅 What Is A Prime Number? 🏅

A Prime Number is divisible by 2 factors: 1 and itself.

Some of you might be planning to answer this question by taking 113 and dividing it by all the numbers below 113.

So you’ll take 113 ÷ 1, 113 ÷ 2, 113 ÷ 3 and so on.

But then some of you might be thinking, “No, that will take too much time.”

Why not try to divide 113 by all the prime numbers between 1 and 113 instead?

Now that sounds like a very good idea. So let’s list down all the prime numbers between 1 and 113:

However, you realise that you will be dealing with a lot of numbers!

Besides that, there’s still one more step you need to do, which is to take 113 and divide it by all the prime numbers you listed.

Now, how do we check if 113 is a prime number?

If 113 is a prime number, it means that it should not be divisible by any of the prime numbers we listed above.

But dividing 113 by all the prime numbers below itself is not the right method to use.

I’m going to teach you a shortcut.

Get your calculators, find the square root of 113 and round it off to the nearest whole number.

It is 10.63, which will give us 11 rounded off to the nearest whole number.

Next, I need you to list down all the prime numbers from 2 to 11.

Instead of the very long list that we had earlier, we are now down to only 5 numbers. We are going to check whether 113 is divisible by these numbers.

Is 113 Divisible By 2?

56.5 is not a whole number.

Therefore, 2 is not a factor of 113.

Is 113 Divisible By 3?

Again, it is not a whole number.

So 3 is not a factor of 113.

Is 113 Divisible By 5?

It is not a whole number, so 5 is not a factor of 113.

Is 113 Divided By 7?

This tells us that 7 is not a factor of 113.

Is 113 Divided By 11?

Therefore, 11 is also not a factor of 113.

Thought Process

Finally, after checking all 5 prime numbers, we can conclude that 113 is a prime number.

Final Answer

113 is a prime number because 113 is not divisible by any prime number below 113.

Conclusion

I hope that after reading this blog post, you have learned a faster way to decide whether a number is a prime number.

Remember these steps:

1️⃣ Find the square root of the number and round it off to the nearest whole number.

📝 It helps to ease the process of proving a prime number.

It removes the need to check whether all numbers up until that number in question are a factor of the number itself.

2️⃣ List down all the prime numbers from 2 to the whole number that you found.

3️⃣ Check whether the number is divisible by the numbers you listed in step 2.

If the number is not divisible by all the numbers you listed, you can conclude that it is a prime number.

Keep a lookout for more S1 Math blog posts!