Page 166 - ABCTE Study Guide_Neat

Previously Covered

• So far, we’ve covered the various types of numbers (real numbers, rational numbers,
irrational numbers, whole numbers, and integers), as well as how they relate to each other
using the common device of a number line.
• We've also discussed the various properties of addition and multiplication.

All whole numbers are categorized as either prime or composite, with the exceptions of zero and one,
which are special cases. Let’s take a look at the difference between prime and composite numbers.

Prime numbers have exactly two factors, one and the number itself.

If you know your divisibility rules (covered in the next section), then determining the prime numbers from
1–100 is a relatively easy task. Here are the prime numbers up to 25:

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

By the way, there is no pattern for finding all of the prime numbers that exist, although mathematicians
have found prime numbers with almost eight million digits. This is one of the remaining big math mysteries
out there for mathematicians.

Composite numbers have more than two factors but not an infinite number of factors.
All even numbers (except the number two) are composite, since they can all be divided by two.

Zero is neither prime nor composite. Since any number times zero equals zero, there are an infinite
number of factors for a product of zero. A composite number must have a finite number of factors.

One is also neither prime nor composite. The only way to get a product of one is by multiplying 1 x 1. But
duplicate factors are only counted once, so one only has one factor. (A prime number has exactly two
factors, so one can’t be prime.)

A typical test question would have you identify which number from a list is prime (or composite or neither).

Try this one:

Question

Which of the follwing is a prime number?

A 33

B 45

C 41

D 51