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Prime Numbers: Lesson for Kids

Instructor: Trisha Fyfe

Trisha has taught college and K-12 English, reading, writing, and math. She has a master's degree in teaching.

Have you ever wondered why some numbers can be divided up evenly and some numbers can't? In today's lesson we will learn why it's hard to divide prime numbers and how to identify them.

Candy Trouble

Tomorrow is your brother Jake's birthday, and you're in charge of filling the goody bags with candy and silly toys. You know that everyone loves goody bags, so you want to be extra careful to fill them equally.

But here's the problem: you have 31 pieces of candy and 10 people are coming to the party. You try again and again to divide the candy up evenly, but every time you put the candy into the bags (it doesn't matter how you split it up), there's at least one piece left over.

What to do? Your math whiz sister tells you it's impossible. The number 31 is a prime number, so there will always be candy left over.

As a prime number, 31 can be divided only 2 ways, by 1 and itself.
30 is a Prime Number

You Can't Break Prime Numbers

A prime number is a number that can be divided by only the number 1 and itself. 31 is a prime number because 31 ÷ 1 = 31 and 31 ÷ 31 = 1 are the only two ways we can divide 31.

Think of it this way: 'prime' means 'excellent' or 'best'. A prime number is so good at being itself that it's hard to break up.

To understand prime numbers well, it's helpful to know about their opposite, composite numbers. Remember, prime numbers can be divided by only 1 and itself. So what would be the opposite of that?

Breakable Composite Numbers

Any number that is not a prime number is a composite number. Composite numbers can be divided into equal groups by more than just 1 and the number itself.

For example, the number 4 is composite. We can divide 4 into several different equal groups. We can make 2 groups of 2, for example, with the division problem: 4 ÷ 2 = 2.

Think of it this way: 'composite' means 'made up of smaller parts', so a composite number is easy to break up.

Is it Prime?

Back to that candy - you need to finish the goody bags! You decide to eat one piece of candy. No one will notice, right? Now you have 30 pieces of candy. But is 30 still a prime number? Let's find out.

You already know 30 can be divided by 1 and itself (30 ÷ 1 = 30 and 30 ÷ 30 = 1).

You decide to find every way possible to divide 30 into groups. You make a list of division problems. When your list is finished, you have 8 solutions listed.

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