Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software


Prime and Composite
Numbers
Unit 3 > Lesson 3 of 9

Problem 1:   The area of a rectangular garden is 7 square yards. List all possible whole-number dimensions the garden can have. [IMAGE]
Solution:   1 yd x 7 yd

The whole-number dimensions, 1 and 7, of the rectangular garden above, are the factors of the number 7.

Problem 2:   The area of a rectangular garden is 8 square yards. List all possible whole-number dimensions the garden can have.
  [IMAGE] [IMAGE]
Solution:   1 yd x 8 yd,  2 yd x 4 yd

The whole-number dimensions, 1, 2, 4 and 8, of the rectangular gardens in Problem 2, are the factors of the number 8. In Problem 1, the number 7 has only two factors. The number 7 is prime. In problem 2 above, the number 8 has four factors. The number 8 is composite.

Definitions

  1. A prime number has only two factors: 1 and itself.
  2. A composite number has more than two factors.
  3. The number 1 is neither prime nor composite.
When the area of a rectangle is a prime number, there is only one set of possible dimensions for that rectangle. When the area of a rectangle is a composite number, there are two or more sets of possible dimensions for that rectangle. Each set of dimensions is a pair of factors.

To determine if a number is prime or composite, follow these steps:

  1. Find all factors of the number.
  2. If the number has only two factors, 1 and itself, then it is prime.
  3. If the number has more than two factors, then it is composite.

Example 1:   Is the number 2 prime or composite?
Solution:   The factors of 2 are 1 x 2
  2 is prime

Example 2:   Is the number 9 prime or composite?
Solution:   The factors of 9 are 1 x 9, 3 x 3
  9 is composite

We have determined if a single number is prime or composite. Let's look at a range of numbers to see if they are prime or composite. Please note that each range of numbers given in Examples 3, 4 and 5 below are inclusive.

Example 3:   Find all prime numbers between 2 and 9.
  factors of 2: 1 x 2 2 is prime
  factors of 3: 1 x 3 3 is prime
  factors of 4: 1 x 4, 2 x 2 4 is composite
  factors of 5: 1 x 5 5 is prime
  factors of 6: 1 x 6, 2 x 3 6 is composite
  factors of 7: 1 x 7 7 is prime
  factors of 8: 1 x 8, 2 x 4 8 is composite
  factors of 9: 1 x 9, 3 x 3 9 is composite
Solution:   The prime numbers between 2 and 9 are 2, 3, 5 and 7.  [IMAGE]

Example 4:   Find all prime numbers between 10 and 19.
  factors of 10: 1 x 10, 2 x 5 10 is composite
  factors of 11: 1 x 11 11 is prime
  factors of 12: 1 x 12, 2 x 6, 3 x 4 12 is composite
  factors of 13: 1 x 13 13 is prime
  factors of 14: 1 x 14, 2 x 7 14 is composite
  factors of 15: 1 x 15, 3 x 5 15 is composite
  factors of 16 1 x 16, 4 x 4 16 is composite
  factors of 17: 1 x 17 17 is prime
  factors of 18: 1 x 18, 3 x 6 18 is composite
  factors of 19: 1 x 19 19 is prime
Solution: The prime numbers between 10 and 19 are 11, 13, 17 and 19.  [IMAGE]

Example 5:   Find all prime numbers between 20 and 29.
  factors of 20: 1 x 20, 2 x 10, 4 x 5 20 is composite
  factors of 21: 1 x 21, 3 x 7 21 is composite
  factors of 22: 1 x 22, 2 x 11 22 is composite
  factors of 23: 1 x 23 23 is prime
  factors of 24: 1 x 24, 2 x 12, 3 x 8, 4 x 6 24 is composite
  factors of 25: 1 x 25, 5 x 5 25 is composite
  factors of 26: 1 x 26, 2 x 13 26 is composite
  factors of 27: 1 x 27, 3 x 9 27 is composite
  factors of 28: 1 x 28, 2 x 14, 4 x 7 28 is composite
  factors of 29: 1 x 29 29 is prime
Solution:   The prime numbers between 20 and 29 are 23 and 29.  [IMAGE]

Example 6:   Is the number 31 prime or composite? Explain your answer using full sentences.  [IMAGE]
Solution 1:   The number 31 is prime because its only factors are one and itself.
Solution 2:   Thirty-one is a prime number. This is because the number 31 has only two factors: 1 and 31.
Solution 3:   I divided the number 31 by all numbers between 1 and 31 and found no factors other than one and thirty-one. Therefore, 31 is prime.

There are many possible ways to explain the solution to this problem. These are just three possible explanations.


Summary:   A prime number has only two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite.
  The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 since each of these numbers has only two factors, itself and 1.


Exercises

Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1. Each of the following numbers is composite EXCEPT:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39
32 and 39
30 and 34
31 and 37
All composite

RESULTS BOX:

2. The prime numbers between 40 and 49 are:
42, 43 and 47
41, 43 and 47
43, 45 and 47
None of the above.

RESULTS BOX:

3. The prime numbers between 50 and 59 are:
53 and 59
51 and 59
53 and 57
None of the above.

RESULTS BOX:

4. The prime numbers between 60 and 69 are:
63 and 69
61 and 67
60 and 65
None of the above.

RESULTS BOX:

5. The prime numbers between 20 and 69 are:
21, 23, 29, 31, 37, 41, 43, 47, 53, 63 and 69
23, 29, 31, 33, 37, 41, 43, 47, 59, 61 and 67
23, 29, 31, 37, 41, 43, 47, 53, 59, 61 and 67
None of the above.

RESULTS BOX:


This lesson is by Gisele Glosser. You can find me on Google.

Elementary Math Lessons
Factors and GCF
Multiples and LCM
Primes and Composites
Divisibility Rules
Exponents
Patterns and Exponents
Practice Exercises
Challenge Exercises
Solutions

Related Activities
Exponents and Scientific Notation
Factor Tree Game
Number Theory WebQuest
Pre-Made Worksheets
Square Root Calculator
Word Search Puzzle
Worksheet Generator


About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 24 Nov 2014