Divisibility Rules

Show your work for each problem.

1.
Which number is divisible by ?
1. a)
2. b)
3. c)
4. d)
Answer:
ends in , which is even, so it is divisible by . The others end in odd digits (, , ).
2.
Which number is divisible by ?
1. a)
2. b)
3. c)
4. d)
Answer:
ends in , so it is divisible by . The others end in , , and , which are neither nor .
3.
What is the sum of the digits of ?
Answer: 12
. This digit sum helps determine divisibility by and .
4.
Is divisible by ? Enter yes or no.
Answer: yes
Digit sum: . Since with no remainder, is divisible by .
5.
Which number is divisible by ?
1. a)
2. b)
3. c)
4. d)
Answer:
ends in , so it is divisible by . The others end in , , and .
6.
Is divisible by ? Show your work.
Answer: yes
1. What is the first digit of 738? 7
2. What is the sum of all digits (7 + 3 + 8)? 18
3. Is 18 divisible by 3? yes
4. So is 738 divisible by 3? yes
7.
Is divisible by ? Enter yes or no.
Answer: yes
The last two digits are . Since with no remainder, is divisible by .
8.
Which number is divisible by both AND (therefore divisible by )?
1. a)
2. b)
3. c)
4. d)
Answer:
ends in (even, so divisible by ) and (divisible by ). Therefore is divisible by . is divisible by but not . is divisible by but not . is divisible by only.
9.
Is divisible by ?
Answer: yes
1. What are the four digits in 1,845? 1, 8, 4, 5
2. What is 1 + 8 + 4 + 5? 18
3. Is 18 divisible by 9? yes
4. Is 1,845 divisible by 9? yes
10.
What are the last two digits of ?
Answer: 36
The last two digits of are . Since , this number is divisible by .
11.
Is divisible by ?
Answer: yes
1. Is 456 divisible by 2? (Does it end in an even digit?) yes
2. What is 4 + 5 + 6? 15
3. Is 15 divisible by 3? yes
4. Since 456 is divisible by both 2 AND 3, is it divisible by 6? yes
12.
Which number is divisible by but NOT by ?
1. a)
2. b)
3. c)
4. d)
Answer:
: digit sum (divisible by ). But ends in (odd), so it's NOT divisible by , therefore NOT by . The others (, , ) are all even and divisible by both and .
13.
Is divisible by ? Enter yes or no.
Answer: yes
The last two digits are . Since with no remainder, is divisible by .
14.
A school has students. Can they form teams of exactly students each with no one left over?
Answer: yes
1. What is the digit sum of 342? (3 + 4 + 2) 9
2. Is 9 divisible by 9? yes
3. Is 342 divisible by 9? yes
4. Can they form complete teams of 9? yes
15.
Which divisibility rules does satisfy: , , , , , , ?
Answer: 2, 3, 4, 5, 6, 9, 10
1. Does 2,340 end in an even digit? (Is it divisible by 2?) yes
2. What is 2 + 3 + 4 + 0? 9
3. Is the digit sum 9 divisible by 3? yes
4. Are the last two digits (40) divisible by 4? yes
5. Does 2,340 end in 0 or 5? (Divisible by 5?) yes
6. Is it divisible by both 2 AND 3? (Divisible by 6?) yes
7. Is the digit sum 9 divisible by 9? yes
8. Does it end in 0? (Divisible by 10?) yes