. Suppose that n is a three-digit natural number, and 3 | n. If x is the 100s digit of n, y is the 10s digit of n, and z is the 1s digit of n, show that 3 | (x y z). (Hint: To understand the notation x, y, and z, suppose, for example, that n is the number 153. In this case, we get x

Proof is shown in the Explanation

Step-by-step explanation:

Suppose that you have a three-digit number natural number n that is written xyz. Then

So when we divide n by 3, we obtain:

The remainder is clearly going to come from the division , since 33x+3y is an integer.

Since 3 divides n, the remainder is going to be a multiple of 3 and so we have shown that 3|(xyz).

Example:

Consider the number 336

by definition, an arc subtended by a central angle of some given measure has the same measure. so .