Chapter 4.1A, Problem 15A

To find the remainder when a number is divided by $3$, you could us long division. Alternatively, you could find the sum of the digits and then find the remainder when that sum is divided by $3$.

a. Find the remainder when $7,242,815$ is divided by $3$, using long division and then using the sum of the digits.

b. Explain why the sum of the digits approach is valid.

c. Will the sum of the digits approach work to find the remainder when a number is divided by $9$? Justify your answer.