Divisibility by 3 and 9

Name:

Class:

Date:

Show your work for each problem.

1.
Which number is divisible by $3$ ?
1. a)535
2. b)770
3. c)421
4. d)612
2.
Which number is divisible by $9$ ?
1. a)6303
2. b)8120
3. c)2346
4. d)5013
3.
Which statement is true?
1. a)Every number divisible by 9 is also divisible by 3
2. b)Every number divisible by 3 is also divisible by 9
3. c)Every number ending in 3 is divisible by 3
4. d)A number is divisible by 9 if its last digit is 9
4.
What is the remainder when $5237$ is divided by $9$ ?
1. a)0
2. b)7
3. c)8
4. d)2
5.
Leo wrote $3456 + 2789 = 6235$ . What does casting out nines tell you?
1. a)The answer is wrong: both sides give remainder 0
2. b)The answer passes the check, so it is correct
3. c)The answer is wrong: the left side gives remainder 8, but 6235 gives 7
4. d)Casting out nines cannot be used for addition
6.
What is the digit sum of $8457$ ?
7.
Add the digits of $98{,}765$ again and again until only one digit is left. Which digit do you get?
8.
The number $6\square51$ is divisible by $9$ . Which digit goes in the box?
9.
What remainder does $6014$ leave when divided by $3$ ?
10.
How many different digits (0 to 9) can go in the box so that $3\square5$ is divisible by $3$ ?
11.
Use the digit sum to show that $741$ is divisible by $3$ , then find $741 \div 3$ .
12.
Use the digit sum to show that $2358$ is divisible by $9$ , then find $2358 \div 9$ .
13.
Use the digit sum to find the remainder when $1234$ is divided by $3$ .
14.
Use repeated digit sums to find the remainder when $879{,}999$ is divided by $9$ .
15.
The number $4\square8$ is divisible by $9$ . Find the missing digit and then work out the division.
16.
Split $372$ as $3 \times 99 + 7 \times 9 + (3 + 7 + 2)$ and use it to find the remainder when $372$ is divided by $9$ .
17.
Check $4782 + 3569 = 8351$ by casting out nines.
18.
Look at $25\square8$ . How many digits make it divisible by $3$ ? Which digit makes it divisible by $9$ ?