# Primes and Composites

**Prime:**A number with exactly two factors; one and itself.

What does this mean? This means that for us to call a number prime, only two whole numbers can divide into it without a remainder.

Here are a few examples:

**2, 3, 5, 7, 11, 13, 17, 19, 23,...**

There are an infinite number of primes. The list could go on and on.

Think about it:

The only whole numbers that divide evenly into 2 are

**1 and 2.**

The only whole numbers that divide evenly into 3 are

**1 and 3.**

The only whole numbers that divide evenly into 5 are

**1 and 5.**

We could keep on going, but we would never be done with the list of primes, so let's move on to Composites.

**Composite:**A number with more than two factors.

This means that something other than 1 and itself must divide evenly into the composite number.

Here are a few examples:

**4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28,...**

There are also an infinite number of composites. This list could also go on and on.

Think about it:

The factors of 4 are 1,

**2**, 4. Notice that there is something in that list other than 1 or 4!

The factors of 6 are 1,

**2, 3**, 6. Notice again that there are things other than 1 and 6 in that list.

As soon as you can list a third factor, you have a composite number!

Did you notice that a certain number is missing?

Where is ?

**1 is not prime or composite.**It only has 1 factor -- itself! You could say that 1 is the loneliest number. It does not fit in either category. It does not have exactly two factors to be a prime and it also does not have more than two factors to be with the composites. So if you are even asked if 1 is prime or composite, you should answer,

**neither**!

**Common Misconceptions:**

All the odds are prime.

This is

**FALSE**! Some odds are prime, like 3, 7, 11...

However, there are primes that have more than 2 factors, like 9. The factors of 9 are 1, 3, and 9. Because there are more than 2 factors, 9 is composite.

All evens are composite.

This is also

**FALSE**. Most evens are composite. However, there is one even that is prime. This would be 2. The only factors of 2 are 1 and 2.

Numbers that end in 1 and 7 are prime.

This is also

**FALSE**. Although there are some numbers that end in 1 or 7 that are prime (like 11, 17, 31, and 37), there are also composite numbers that end in 1 and 7.

These numbers are often called "fake primes" because they look prime, but they aren't. Here are some examples: 51, 57, 81, 87, 91.

Let's take a look at why they are composite.

**3**, 17, 51

Factors of 57: 1,

**3**, 19, 57

Factors of 81: 1,

**3**, 9, 9, 27, 81

Factors of 87: 1,

**3**, 29, 87

**7**, 13, 91

When three doesn't work, you should also try 7 to get rid of more fake primes.

**Let's Review:**Prime numbers have exactly two factors: 1 and itself. Composites have more than two factors. The number 1 is neither prime nor composite. Finally, if you are trying to figure out if an odd number is a prime, test to see if the number is divisible by primes like 3 and 7 first. This will help you get rid of most of the fake primes.

**Related Links:**

Math

Fractions

Factors