Chapter 5, Problem 1T

In Exercises 1-6, decide whether each statement is true or false.

For all natural numbers n, 1 is a factor of n, and n is a multiple of n.

To determine

Whether the statement “For all natural numbers $n$, 1 is a factor of $n$, and $n$ is a multiple of n” is true or false.

Answer to Problem 1T

Solution:

The statement “For all natural numbers $n$, 1 is a factor of $n$, and $n$ is a multiple of n” is true.

Explanation of Solution

The 1 is a universal factor of $n$, and $n$ is a multiple of $n$.

For example:

Let’s take any natural number $n$.

The natural number $n=19$.

When $n=19$ divided by 1,

$19÷1=19$

The 19 is completely divided by 1, hence 1 is a factor of 19.

Also, 19 is divisible by 19 itself. (In fact, any natural number is divisible by itself.)

$19÷19=1$

For any natural number $n$, it is true that 1 is a factor of $n$, and $n$ is a multiple of n.