# What Are Prime Numbers? - Definition & Examples

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• 0:05 Factors
• 0:29 Prime Numbers
• 1:31 Some Prime number Rules
• 3:33 Some More Prime Numbers
• 4:30 Lesson Summary

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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, we'll do a brief review of factors, and then learn how factors make prime numbers unique. You can also test your knowledge with a brief quiz.

## Factors

Before we discuss prime numbers, let's quickly review what factors are. Factors are simply two numbers you multiply together to get a product. For example, in the number sentence:

3 * 2 = 6

3 and 2 are the factors, and 6 is the product. Likewise, in this number sentence:

50 * 40 = 2,000

50 and 40 are the factors, and 2,000 is the product.

## Prime Numbers

Now let's consider the number 2. There's only one pair of factors we can use to get a product of 2:

2 * 1 = 2

No other factors, when multiplied together, will give us 2.

Let's look at 3. There are only two factors that will give us 3:

3 * 1 = 3

Therefore, 2 and 3 are prime numbers because a prime number is one that has only two factors: 1 and itself. For example, we've discovered that the only factors for 2 are 1 and 2 (itself). Likewise, the only factors for 3 are 1 and 3 (itself). Let's go ahead and consider 4. 4 and 1 are definitely factors:

4 * 1 = 4

But that's not the only factor pair for 4 because we can also do this:

2 * 2 = 4

Therefore, 4 has more than two factors, so it is not a prime number.

## Some Prime Number Rules

Rule Number 1: Since even numbers are always divisible by 2, no even number (other than 2) can be a prime number because they'll always have more than two factors. They'll have 1 and themselves, and they'll also have 2 and some other factor. For example, the factor pairs for 6 are:

6 * 1 = 6
3 * 2 = 6

6 has four factors and therefore is not a prime number.

Rule Number 2: Numbers that end in 5 or 0 are always divisible by 5. So no numbers divisible by 5 (other than 5) can be prime numbers because they'll always have more than two factors. They'll have 1 and themselves, and they'll also have 5 and some other factor. For example, the factor pairs for 15 are:

15 * 1 = 15
3 * 5 = 15

15 has four factors and, therefore, is not a prime number. And the factor pairs for 20 are:

20 * 1 = 20
10 * 2 = 20
5 * 4 = 20

20 has six factors and therefore is not a prime number.

Rule Number 3: 0 and 1 are not prime numbers. It may seem at first glance that they are, but remember that a prime number has only 1 and itself as factors. But 0 has an infinite number of factors because 0 * 1 = 0, and 0 * 2 = 0, and 0 * 3 = 0, and so on. So 0 is far from prime.

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