Chapter 4.1, Problem 60E

To determine

To find the factors of given number using prime factorization.

Answer to Problem 60E

  $1,2,4,5,10,20,25,50,100,125,250,and500.$

Explanation of Solution

Given Information: 500

Formula used: Calculate the factors by dividing every possible number. Then take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1.

Calculation:

Since the Factors of 500 are all the numbers that can evenly divide into 500, simply need to divide 500 by all numbers up to 500 to see which ones result in an even quotient.

  $\begin{array}{l}500÷1=500\\ 500÷2=250\\ 500÷4=125\\ 500÷5=100\\ 500÷10=50\\ 500÷20=25\\ 500÷25=20\\ 500÷50=10\\ 500÷100=5\\ 500÷125=4\\ 500÷250=2\\ 500÷500=1\end{array}$

The Positive Factors of 500are therefore all the numbers used to divide (divisors) above to get an even number. Here is the list of all Positive Factors of 500 in numerical order:

  $1,2,4,5,10,20,25,50,100,125,250,and500.$