# Climbing Down Trees

## OBJECTIVE: To learn how to do prime factorization using tree diagrams

﻿ With the exception of 1 and 0, whole numbers (or nonnegative integers) can be classified as either prime or composite. A whole number is regarded as prime if its only factors are 1 and itself. The smallest and the only even prime number is 2; the rest are odd. A whole number greater than 1 that is NOT prime is composite. Prime factorization is the process of finding the prime factors of a given composite number. Start by dividing the number by the smallest prime factor by which it can be divided. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, ... Repeat the process using successively larger prime factors until all the numbers at the end of each branch are prime. Enter a number in the box at the upper left-hand corner of the applet below. Watch intently as the prime factors of the number are generated in the form of a tree diagram. Note : Use the mouse to pan the viewing frame below if the lower branches are outside the frame.

## Applet by Ethan Hall

It is customary to write the prime factors of a composite number in exponential notation. Example: Instead of writing the prime factorization of 252 as 2 x 2 x 3 x 3 x 7, it may be written in a more compact form as 2² x 3² x 7. Below is a set of problems that require you to find the prime factors of whole numbers. You may construct the tree diagram on a separate sheet or use the applet above. Then check the Answer Box below for the correct answers. Make sure to write your answer in exponential form.

Check out the answers to the above problems here.

## TODAY you learned how to do prime factorization of whole numbers using the tree diagram.

In future lessons, you'll learn how to factor polynomials. Hope you had FUN today!