Chapter 8.1, Problem 28PPS

(a)

To determine

To find: The ladder diagram, and record six whole numbers, two of which are prime.

Answer to Problem 28PPS

The six whole number, and two prime numbers are given in the Figure $\left(1\right)$ .

Explanation of Solution

Given information:

Given the ladder diagram.

  

Calculation:

The numbers for the non prime numbers, selected numbers are $8$ , $15$ , $24$ , and $50$ .

And the selected prime numbers are $11$ , and $23$ .

  

Figure $\left(1\right)$

Therefore, the six whole numbers, and two prime numbers are given in the Figure $\left(1\right)$ .

(b)

To determine

To find: The quotient is $1$ of selected numbers.

Answer to Problem 28PPS

The selected numbers are divided until the quotient is $1$ in Figure $\left(2\right)$

Explanation of Solution

Given information:

Given that divide the two numbers And keep dividing by prime factors until the quotient is $1$ .

Calculation:

Dividing the numbers until the quotient is $1$ .

  

Therefore, the selected numbers are divided until the quotient is $1$ in Figure $\left(2\right)$ .

(c)

To determine

To find: The prime factorization of the six numbers.

Answer to Problem 28PPS

The prime factorization of the numbers is given below.

Explanation of Solution

Given information:

The selected numbers

Calculation:

The prime factorizations of the our selected numbers are

  $\begin{array}{c}8=2^3\\ 15=3.5\\ 24=2^3.3\\ 50={2.5}^2\\ 11=11\\ 23=23\end{array}$

Therefore, the prime factorization of the numbers is given above.