Chapter 4.1, Problem 44E

To determine

To write the prime factorisation of the given number.

Answer to Problem 44E

7, 31

Explanation of Solution

Given Information: Number 217

Formula used: Start by dividing the number by the first prime number 2 and continue dividing by 2 until you get a decimal or remainder. Then divide by 3, 5, 7, etc. until the only numbers left are prime numbers. Lastly, write the numbers as the product of the prime numbers.

Calculation:

To get the Prime Factors of 217, you divide 217 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 217. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 217. Here is the math to illustrate:

  $\begin{array}{l}217÷7=31\\ 31÷31=1\end{array}$

Again, all the prime numbers you used to divide above are the Prime Factors of 217. Thus, the Prime Factors of 217 are:

7, 31.