Hello and welcome to Tutoring Hour!
In this video, we'll take a look at what prime numbers and composite numbers are, and how to identify them.
Let’s first figure out what the two mean
A composite number can be divided exactly by a whole number other than 1 and itself,
While a prime number can’t be divided by any number other than 1 and itself.
Imagine you have 6 donuts and you wanna share them.
Let’s figure out in how many different ways this can be done.
We can make 2 groups with 3 donuts in each
Or 3 groups of 2 donuts each
Or 6 groups with 1 donut in each
Let’s view this mathematically.
We can express 6 as 2 times 3, 3 times 2
Or 6 times 1
How would you share 9 donuts?
We can obviously group them into 9 groups of 1,
We can also divide the donuts evenly into 3 groups of 3 donuts each.
Now, imagine there were 7 donuts.
How would you share them?
We can share the 7 donuts by putting them into 7 groups of 1 each.
There’s no other way to divide the 7 donuts into equal groups without having any left over.
The numbers 6 and 9 could be divided by other whole numbers.
But 7 could only be divided by 1 or itself.
From this we understand that 6 and 9 are composite numbers,
And 7 is a prime number.
Let’s take a look at the first few prime and composite numbers.
Take the number 1 for instance. It is neither prime nor composite.
Let’s move to our next number: 2.
It has only two factors, which are: 1 and 2.
You may be wondering what factors are.
They are nothing but the numbers you multiply to get another number.
We multiply 1 and 2 to get the number 2.
So, 1 and 2 are the factors of 2.
Now, let’s check the number: 3.
3 has two factors, and they are: 1 and 3.
Our next number: 4 has 3 factors: 1, 2, and 4,
While the number 5, has just two factors: 1 and 5.
And, the number 6 has 4 factors: 1, 2, 3, and 6.
Look at the numbers here, some have two factors, and some have more than two.
The numbers that have just two factors: 1 and the number itself, are called prime numbers.
The numbers that have more than two factors are called composite numbers.
But with larger numbers, the quickest way to find the factors is by using the divisibility rules.
If you are not sure of what they are, go ahead and find the link to our video on Divisibility Rules in the description box.
Moving on
Let’s show you an interesting way of finding prime numbers using the Sieve of Eratosthenes.
We’ll use this chart with numbers 1 to 50
Let’s cross out 1 in green. We know it is neither prime nor composite
2 we know is a prime number. In fact it is the only even prime number.
Now, let’s cross out all the multiples of 2.
In other words, all even numbers, since they are divisible by 2.
3 is our next prime number.
We'll cross out all its multiples.
5 is a prime. We need to cross out its multiples as well.
We’ll highlight 7 and eliminate its multiples.
All the numbers that are crossed out in red are composite.
And the numbers left uncrossed are obviously prime.
We have clued you enough on how to find the prime and composite numbers between 1 and 50.
Go ahead and extend this method to any number, and scout out the prime and composite numbers in no time.
There is nothing like good practice to fill the gap between learning and doing.
If you guys got some time on hand, and think you must practice this stuff,
Then visit our website tutoringhour.com.
Check the link in the description box. Download the worksheets, and get started!
Don’t forget to like our channel.
And hit the subscribe button, if you haven’t already done that!
Thank you guys for watching Tutoring Hour!