Question

let the natural number n have the decimal numeral 123,460,38d, where d is the units digit. use divisibility tests to answer parts (a) through (h) below.

(a) for what value(s) of d is n divisible by 2?
0,2,4,6,8 (use a comma to separate answers as needed.)

(b) for what value(s) of d is n divisible by 3?
0,3,6,9 (use a comma to separate answers as needed.)

(c) for what value(s) of d is n divisible by 4?
0,4,8 (use a comma to separate answers as needed.)

(d) for what value(s) of d is n divisible by 5?
0,5 (use a comma to separate answers as needed.)

(e) for what value(s) of d is n divisible by 6?
(use a comma to separate answers as needed.)

Explanation:

Analyze the number and divisibility criteria

Using the Divisibility Rules knowledge point

$$ n = 123,460,38d $$

For \(n\) to be divisible by 6, it must be divisible by both 2 and 3.

Determine divisibility by 2

Using the Divisibility Rules knowledge point

$$ d \in \{0, 2, 4, 6, 8\} $$

Determine divisibility by 3

Using the Divisibility Rules knowledge point

$$ 1+2+3+4+6+0+3+8+d = 27 + d \implies d \in \{0, 3, 6, 9\} $$

Find the intersection for divisibility by 6

Using the Divisibility Rules knowledge point

$$ d \in \{0, 2, 4, 6, 8\} \cap \{0, 3, 6, 9\} = \{0, 6\} $$

Answer:

(e) For what value(s) of d is n divisible by 6?

<blank>0,6</blank> (Use a comma to separate answers as needed.)