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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