Simon is working on a riddle.

“I am a number between 1 and 50. The sum of my digits is not prime, but I myself am prime. In a year, you will only see me 7 times. What number am I?”

How can Simon solve the riddle?

In this concept, you will learn how to classify a number as a prime or composite number.

### Classifying Prime and Composite Numbers

Numbers can be classified into two categories. The number of factors that a number has determines whether the number is considered a **prime number** or a **composite number**.

Prime numbers are special numbers that are greater than 1 and only have two factors: 1 and the prime number itself. Composite numbers are numbers that have more than two factors. Most numbers are composite numbers.

Here is a prime number.

13

The factors of 13 are only 1 and 13. Therefore, 13 is a prime number. Here is a chart of prime numbers. There are 25 prime numbers between 1 and 100. Take a few minutes to take some notes on prime and composite numbers. Be particularly careful when considering the number “1”. One is neither prime nor composite.

Here is a composite number.

44

The factors for 44 is 1, 2, 4, 11, 22, and 44. Therefore, 44 is a composite number; it is made up of more than two factors.

### Examples

#### Example 1

Earlier, you were given a problem about Simon’s riddle.

Use the prime number cart to help solve the riddle. “I am a number between 1 and 50. The sum of my digits is not prime, but I myself am prime. In a year, you will only see me 7 times. What number am I?

First, look at the numbers between 1 an 50 that are prime. There are 15 prime numbers.

Then, eliminate the numbers where the sum of the digits is prime.

Next, find the number you only see 7 times a year. Think about a calendar. 37 is not on a calendar at all. You see 11, 13, 17, 19 more than 7 times in a year.

The answer to the riddle is 31.

#### Example 2

Prove that 91 is a prime number.

First, list all the factors of 91. 91 at the very least has the factors 1 and 91. Keep looking for other factors.

Not 2, 3, 4, 5, 6. Let’s divide 91 by 7.

91 also has the factors 7 and 13.

91 is not a prime number. It is a composite number.

#### Example 3

If a number has more than two factors, the number is prime. True or false?

False, numbers with more than two factors are composite numbers.

#### Example 4

The operation associated with factors is addition. True or false?

False, the operation associated with factors is multiplication.

#### Example 5

Why is 29 a prime number?

29 is a prime number because the only two factors for 29 are 1 and 29.

### Review

Identify the following values as prime or composite.

- 12
- 10
- 15
- 16
- 56
- 18
- 20
- 22
- 23
- 25
- 27
- 31
- 81
- 48
- 24
- 30

### Review (Answers)

To see the Review answers, open this PDF file and look for section 5.3.