Chapter 5, Problem 1RE

In Exercises 1 and 2, determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, 10, and 12. If you are using a calculator, explain the divisibility shown by your calculator using one of the rules of divisibility.

238,632

To determine

To calculate: The numbers that can divide $238,632$.

Answer to Problem 1RE

Solution: $2,3,4,6,8\text{and}12.$

Explanation of Solution

Given: The numbers $2,3,4,5,6,8,9,10\text{and}12$

Calculation:

Write $238,632$ in terms of prime factors as follows:

$238,632=2\times 2\times 2\times 3\times 61\times 163$

Now, check which of the provided numbers can be obtained by multiplying the prime factors of $238632$ as follows:

$\begin{array}{l}2=2\\ 3=3\\ 4=2\times 2\\ 5=\text{cannot be obtained}\end{array}$

$\begin{array}{l}6=2\times 3\\ 8=2\times 2\times 2\end{array}$

$\begin{array}{l}9=3\times 3\left(\text{cannot be obtained}\right)\\ 10=2\times 5\left(\text{cannot be obtained}\right)\\ 12=2\times 2\times 3\end{array}$

So, the numbers that can divide $238,632$ are $2,3,4,6,8\text{and}12.$