Factors and Multiples

Show your work for each problem.

1.
Which number is a factor of 20?
1. a)6
2. b)8
3. c)3
4. d)4
Answer: 4
with no remainder, so 4 is a factor of 20. The other options: , , .
2.
Which number is a multiple of 6?
1. a)16
2. b)30
3. c)34
4. d)22
Answer: 30
, so 30 is a multiple of 6. The other options: , , .
3.
How many factors does 12 have?
Answer: 6
The factors of 12 are: . That's 6 factors in total.
4.
What is the third multiple of 7?
Answer: 21
The multiples of 7 are: The third multiple is .
5.
Which statement is TRUE?
1. a)21 is a multiple of 21 only
2. b)7 is a multiple of 21
3. c)21 is a factor of 7
4. d)7 is a factor of 21
Answer: 7 is a factor of 21
, so 7 is a factor of 21. This also means 21 is a multiple of 7.
6.
What is the largest factor of 24 that is less than 24?
Answer: 12
The factors of 24 are: . The largest one less than 24 is 12.
7.
Which number is both a factor of 36 AND a multiple of 3?
1. a)10
2. b)9
3. c)4
4. d)8
Answer: 9
9 is a factor of 36 () AND 9 is a multiple of 3 (). 4 is a factor of 36 but not a multiple of 3. 8 and 10 are not factors of 36.
8.
Find all the factors of 28.
Answer: 1, 2, 4, 7, 14, 28
1. What is ? 28
2. What is ? 14
3. Is 28 divisible by 3? (yes/no) no
4. What is ? 7
5. Now list all the factors in order: 1, 2, 4, 7, 14, 28
9.
List the first 6 multiples of 8.
Answer: 8, 16, 24, 32, 40, 48
1. What is ? 8
2. What is ? 16
3. What is ? 24
4. What is ? 32
5. What is ? 40
6. What is ? 48
10.
A number has exactly 4 factors: 1, 2, 4, and itself. What is the number?
Answer: 8
The number is 8. Its only factors are . If we tried 12, it would have factors which is 6 factors.
11.
You have 30 apples to put into bags. Each bag must have the same number of apples. What are all the possible ways to divide them?
Answer: 1, 2, 3, 5, 6, 10, 15, 30
1. This problem asks for all the factors of what number? 30
2. Can you put all 30 in 1 bag? (yes/no) yes
3. Can you make bags of 2? How many bags? 15
4. Can you make bags of 4? (yes/no) no
5. List all the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
12.
How many factors does 36 have?
1. a)9
2. b)8
3. c)7
4. d)6
Answer: 9
The factors of 36 are: . That's 9 factors. Note that 6 appears only once (not twice) in the pair .
13.
What is the smallest multiple of 7 that is greater than 50?
Answer: 56
Multiples of 7: Since is less than 50, the answer is .
14.
Bus A arrives every 12 minutes. Bus B arrives every 8 minutes. If both buses arrive at 3:00 PM, when will they both arrive together again?
Answer: 3:24 PM
1. List the first 5 multiples of 12: 12, 24, 36, 48, 60
2. List the first 5 multiples of 8: 8, 16, 24, 32, 40
3. What is the smallest common multiple? 24
4. Add 24 minutes to 3:00 PM. What time is it? 3:24 PM
15.
Find all common factors of 24 and 36.
Answer: 1, 2, 3, 4, 6, 12
1. List all factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
2. List all factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
3. Which factors appear in BOTH lists? 1, 2, 3, 4, 6, 12
4. What is the largest common factor (GCF)? 12
16.
What is the smallest number that is both a multiple of 4 and a multiple of 6?
Answer: 12
Multiples of 4: Multiples of 6: The smallest common multiple (LCM) is 12.