Combined Divisibility Rules

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Show your work for each problem.

1.
Which pair of tests together proves that a number is divisible by $12$ ?
1. a)2 and 6
2. b)3 and 4
3. c)3 and 6
4. d)2 and 3
2.
A number is divisible by $2$ and by $9$ . Which number between $10$ and $20$ must also divide it?
3.
Is $2412$ divisible by $12$ ? Use the tests for 3 and 4, then find the quotient.
4.
Which number is divisible by $11$ ?
1. a)3542
2. b)9091
3. c)4825
4. d)6170
5.
Find the alternating sum of $2816$ , starting with $+$ at the ones digit: $6 - 1 + 8 - 2$ .
6.
Is $735$ divisible by $15$ ? Use the tests for 5 and 3, then find the quotient.
7.
$18$ is divisible by $2$ and by $6$ , but not by $12$ . Why?
1. a)2 and 6 share the factor 2
2. b)18 is smaller than 2 × 12
3. c)6 is not a factor of 12
4. d)12 has no divisibility rule
8.
Find the digit $d$ that makes $7d4$ divisible by $18$ .
9.
Is $61{,}809$ divisible by $11$ ? Use the alternating sum, then find the quotient.
10.
Is $4374$ divisible by $18$ ? Use the tests for 2 and 9, then find the quotient.
11.
Which number is divisible by $36$ ?
1. a)2466
2. b)2556
3. c)4518
4. d)1236
12.
How many of the numbers $2, 3, 4, 5, 6, 8, 9, 10, 11, 12$ divide $4620$ ?
13.
$4530$ is divisible by $2$ and by $6$ . Is it divisible by $12$ ? Check with the coprime pair 3 and 4.
14.
Which digit $d$ makes $4d52$ divisible by $36$ ?
1. a)9
2. b)3
3. c)7
4. d)4
15.
Quick factor search: how many of the numbers $2, 3, 4, 5, 6, 8, 9, 10, 11, 12$ divide $2520$ ?
16.
$33 = 3 \times 11$ . Find the digit $d$ that makes $8d14$ divisible by $33$ .
17.
Find the digit $d$ that makes $52d6$ divisible by $12$ .
18.
$132 = 11 \times 12$ . Is $7128$ divisible by $132$ ? Check 11 and 12, then find the quotient.