Chapter 4.1, Problem 15E

To determine

To find the correct value for the prime factorisation of the number 60.

Answer to Problem 15E

  $2\times 2\times 3\times 5$

Explanation of Solution

Given Information: Number 60

Calculation: The main reason for the error of the given answer is the number 4. Since 4 is not a prime number and this has not reached to the smallest prime number of 4(i.e. 2) hence it cannot be used in defining prime factorisation of that number.

To get the Prime Factors of 60, you divide 60 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1.

This Prime Factorization process creates the Prime Factor Tree of 60. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 60. Here is the math to illustrate:

  $\begin{array}{c}60÷2=30\\ 30÷2=15\\ 15÷3=5\\ 5÷5=1\end{array}$

Again, all the prime numbers you used to divide above are the Prime Factors of 60. Thus, the Prime Factors of 60 are:

  $2\times 2\times 3\times 5$