Chapter 5, Problem 1T

Which of the numbers 2, 3, 4, 5, 6, 8, 9, 10, and 12 divide 391,248?

To determine

To calculate: The numbers that can divide $391,248$.

Answer to Problem 1T

Solution: $2,3,4,6,8,9and12$

Explanation of Solution

Given: The numbers $2,3,4,5,6,8,9,10and12$.

Calculation:

Write 391248 in terms of prime factors as follows:

$391,248=2\times 2\times 2\times 2\times 3\times 3\times 11\times 13\times 19$

Now, check which of the provided numbers can be obtained by multiplying the prime factors of $391,248$ as follows:

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

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

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

So, the numbers that can divide 391248 are $2,3,4,6,8,9and12$.