A Quick Look Back

Okay. Let's look at the different sets of numbers before we look at some special ones.

Real Numbers: All the numbers on a number line in any direction, positive or negative.

Natural Numbers: All of the positive whole numbers without zero. {1, 2, 3, 4, 5, ...}

Whole Numbers: Natural numbers and zero. {0, 1, 2, 3, 4, ...}

Integers: All of the whole numbers on the number line and their opposites. {... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

Rational Numbers: Any number that can be expressed or rewritten as a fraction with two integers. You can't have 0 as the denominator of the fraction.

Prime Numbers

That's a pretty long list of possible numbers. We haven't included all of the numbers yet, but you have enough to work with for the next few sections. Within those sets and groups of numbers, you will find some special ones. Prime numbers are a special group of whole numbers. A prime number is a number that can only be divided by one and itself with no remainder. When we talk about the divisors of a prime number, we are always talking about natural numbers (whole numbers greater than 0).

Examples of Prime Numbers: 2, 3, 5, 7, 11

Can a negative numbers be a prime number? No. Negative numbers are not natural numbers. That means no fractions either.

Can zero be a prime number? No. You need two divisors to make a prime. While zero can be divided by any number, you cannot divide by zero.

Is one a prime number? No. You need two divisors to make a prime (one and itself). Technically, one only has one divisor and is not a prime number.

Let's look at a prime number like 13 for a moment. If you divide 13 by either 1 or 13, you are good. It's a nice and easy division problem with no remainders. If you try to divide 13 by 5, you get a remainder of 3. It doesn't matter what you try, the only two numbers that will work are 1 and 13. The only factors of 13 are 1 and 13. Therefore, 13 is a prime number.

• Ways to get 13: (1x13) or (13x1)
• Factors of 13: 1, 13

Let's look at 14 now. If you divide 14 by either 1 or 14, you get nice even answers. What about other numbers? Let's start with 2. 14√∑2 is 7. That means 2 and 7 divide into 14 without a remainder. The numbers 2 and 7 show there are four factors of 14. Since 14 has more than two factors, 14 is not prime. You could say that two whole numbers other than 1 and 14 can be multiplied together to make 14. Therefore, 14 is a composite number.

• Ways to get 14: (1x14), (14x1), (2x7), (7x2)
• Factors of 14: 1, 2, 7, 14 (take a look - there are only two prime factors)

Before We Go...

Is 0 a prime number? No. 0 is neither a prime nor a composite number.

Is 13 real, natural, whole, rational, and prime? Yes. Since it is rational, it is also an integer.

Is 14 real, natural, whole, rational, and prime? No. 14 is a composite number, because two numbers other than 1 and itself can be multiplied to make 14 (2 and 7).


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