Divisibility by 2, 5, and 10

Show your work for each problem.

1.
Which number is divisible by 2?
1. a)84
2. b)91
3. c)37
4. d)53
Answer: 84
ends in , which is even, so is divisible by . The other numbers end in odd digits (, , ).
2.
Which number is divisible by 5?
1. a)72
2. b)67
3. c)83
4. d)145
Answer: 145
ends in , so it's divisible by . . The other numbers don't end in or .
3.
Which number is divisible by 10?
1. a)135
2. b)95
3. c)82
4. d)240
Answer: 240
ends in , so it's divisible by . . Note that ends in , which makes it divisible by but NOT by .
4.
What is the last digit of a number that is divisible by 10?
Answer: 0
All numbers divisible by end in . Examples: , , , , . This is the key rule for divisibility by .
5.
Is 356 divisible by 2? Answer yes or no.
Answer: yes
Yes! ends in , which is even. Therefore is divisible by . We can verify: .
6.
Which number is divisible by BOTH 2 and 5?
1. a)42
2. b)35
3. c)90
4. d)65
Answer: 90
ends in , which is both even (divisible by ) and either or (divisible by ). So is divisible by both! and are only divisible by . is only divisible by .
7.
Is 475 divisible by 10? Answer yes or no.
Answer: no
No! ends in , not . It IS divisible by (), but it is NOT divisible by . For divisibility by , the number must end in .
8.
How many of these numbers are divisible by 5: 120, 73, 85, 42, 100?
Answer: 3
Three numbers are divisible by : (ends in ), (ends in ), and (ends in ). The numbers and do not end in or .
9.
A number is divisible by 10. What else MUST be true about this number?
1. a)It is divisible by 3
2. b)It is divisible by 2 and 5
3. c)It ends in 5
4. d)It is divisible by 7
Answer: It is divisible by 2 and 5
Since , any number divisible by must also be divisible by both and . For example, , , and .
10.
Determine which of the divisors 2, 5, and 10 divide evenly into 680.
Answer: 2, 5, and 10
1. What is the last digit of 680? 0
2. Is 0 an even number? (yes/no) yes
3. So is 680 divisible by 2? (yes/no) yes
4. Is 0 equal to 0 or 5? (yes/no) yes
5. So is 680 divisible by 5? (yes/no) yes
6. Is 680 divisible by 10? (yes/no) yes
11.
Test if 1,254 is divisible by 2, 5, or 10.
Answer: Only by 2
1. What is the last digit of 1,254? 4
2. Is 4 even? (yes/no) yes
3. So is 1,254 divisible by 2? (yes/no) yes
4. Is 4 equal to 0 or 5? (yes/no) no
5. So is 1,254 divisible by 5? (yes/no) no
6. Is 1,254 divisible by 10? (yes/no) no
12.
Find the smallest 3-digit number that is divisible by both 2 and 5.
Answer: 100
To be divisible by both and , a number must be divisible by (end in ). The smallest 3-digit number is . It ends in , so is divisible by , , and .
13.
Maria has 375 stickers. She wants to put them into packs. Which pack size will have NO leftover stickers?
1. a)Packs of 10
2. b)Packs of 5
3. c)All of the above
4. d)Packs of 2
Answer: Packs of 5
ends in . This means it's divisible by ( packs) but NOT by or . Packs of would leave sticker. Packs of would leave stickers.
14.
A school has 2,350 students. Can they be divided into groups of 2? Groups of 5? Groups of 10?
Answer: Yes to all three
1. What is the last digit of 2,350? 0
2. Is 0 even? (yes/no) yes
3. Can they form groups of 2? (yes/no) yes
4. Is 0 equal to 0 or 5? (yes/no) yes
5. Can they form groups of 5? (yes/no) yes
6. Can they form groups of 10? (yes/no) yes
15.
Find the largest 2-digit number divisible by 10.
Answer: 90
1. What is the largest 2-digit number? 99
2. Is 99 divisible by 10? (yes/no) no
3. What must a number end in to be divisible by 10? 0
4. What is the largest 2-digit number ending in 0? 90
16.
The number 4,58_ is divisible by 10. What digit goes in the blank?
Answer: 0
For a number to be divisible by , it must end in . So the missing digit is , making the number . We can verify: .