Factors and Multiples Worksheets - Math Monks - Free Printable

Worksheet on Factors and Multiples

#### Problem 1: Write the first five multiples of the following numbers.

a. 4
- The multiples of a number are obtained by multiplying it by positive integers (1, 2, 3, ...).
- First five multiples of 4:
\[
4 \times 1 = 4, \quad 4 \times 2 = 8, \quad 4 \times 3 = 12, \quad 4 \times 4 = 16, \quad 4 \times 5 = 20
\]
- Answer: 4, 8, 12, 16, 20

b. 13
- First five multiples of 13:
\[
13 \times 1 = 13, \quad 13 \times 2 = 26, \quad 13 \times 3 = 39, \quad 13 \times 4 = 52, \quad 13 \times 5 = 65
\]
- Answer: 13, 26, 39, 52, 65

c. 19
- First five multiples of 19:
\[
19 \times 1 = 19, \quad 19 \times 2 = 38, \quad 19 \times 3 = 57, \quad 19 \times 4 = 76, \quad 19 \times 5 = 95
\]
- Answer: 19, 38, 57, 76, 95

d. 9
- First five multiples of 9:
\[
9 \times 1 = 9, \quad 9 \times 2 = 18, \quad 9 \times 3 = 27, \quad 9 \times 4 = 36, \quad 9 \times 5 = 45
\]
- Answer: 9, 18, 27, 36, 45

---

#### Problem 2: Write four common multiples of the following numbers.

a. 4 and 5
- To find common multiples, list the multiples of each number and identify the ones they have in common.
- Multiples of 4: \(4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, \ldots\)
- Multiples of 5: \(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, \ldots\)
- Common multiples: \(20, 40, 60, 80, \ldots\)
- Four common multiples: 20, 40, 60, 80

b. 3 and 6
- Multiples of 3: \(3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, \ldots\)
- Multiples of 6: \(6, 12, 18, 24, 30, 36, 42, 48, 54, 60, \ldots\)
- Common multiples: \(6, 12, 18, 24, 30, 36, \ldots\)
- Four common multiples: 6, 12, 18, 24

c. 5 and 10
- Multiples of 5: \(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, \ldots\)
- Multiples of 10: \(10, 20, 30, 40, 50, 60, 70, 80, 90, 100, \ldots\)
- Common multiples: \(10, 20, 30, 40, 50, 60, \ldots\)
- Four common multiples: 10, 20, 30, 40

---

#### Problem 3: Find all the factors of the following numbers using the multiplication method.

a. 72
- Factors are numbers that divide 72 exactly without leaving a remainder.
- Use pairs of numbers whose product is 72:
\[
1 \times 72 = 72, \quad 2 \times 36 = 72, \quad 3 \times 24 = 72, \quad 4 \times 18 = 72, \quad 6 \times 12 = 72, \quad 8 \times 9 = 72
\]
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

b. 98
- Use pairs of numbers whose product is 98:
\[
1 \times 98 = 98, \quad 2 \times 49 = 98, \quad 7 \times 14 = 98
\]
- Factors of 98: 1, 2, 7, 14, 49, 98

---

#### Problem 4: Find all the factors of 25 using the division method.

- Factors are numbers that divide 25 exactly without leaving a remainder.
- Test divisibility by integers starting from 1 up to \(\sqrt{25} = 5\):
- \(25 \div 1 = 25\) (remainder 0) → Factors: 1, 25
- \(25 \div 2 = 12.5\) (not an integer)
- \(25 \div 3 = 8.33\) (not an integer)
- \(25 \div 4 = 6.25\) (not an integer)
- \(25 \div 5 = 5\) (remainder 0) → Factors: 5
- Factors of 25: 1, 5, 25

---

Final Answers:

1. First five multiples:
- a. 4, 8, 12, 16, 20
- b. 13, 26, 39, 52, 65
- c. 19, 38, 57, 76, 95
- d. 9, 18, 27, 36, 45

2. Four common multiples:
- a. 20, 40, 60, 80
- b. 6, 12, 18, 24
- c. 10, 20, 30, 40

3. Factors using multiplication method:
- a. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- b. 1, 2, 7, 14, 49, 98

4. Factors using division method:
- 1, 5, 25

Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{1. a. 4, 8, 12, 16, 20} \\
\text{ b. 13, 26, 39, 52, 65} \\
\text{ c. 19, 38, 57, 76, 95} \\
\text{ d. 9, 18, 27, 36, 45} \\
\text{2. a. 20, 40, 60, 80} \\
\text{ b. 6, 12, 18, 24} \\
\text{ c. 10, 20, 30, 40} \\
\text{3. a. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72} \\
\text{ b. 1, 2, 7, 14, 49, 98} \\
\text{4. 1, 5, 25}
\end{array}
}
\]