Factors and Multiples Worksheets - Math Monks - Free Printable

Problem Analysis and Solution

The worksheet consists of three main tasks. Let's solve each one step by step.

---

Task 1: Fill in the table below

The table has three columns:
1. NUMBER: A list of numbers (3, 30, 6, 12, 20).
2. FACTOR OF 15?: Determine if the number is a factor of 15.
3. MULTIPLES OF 3?: Determine if the number is a multiple of 3.

#### Step-by-Step Solution:

1. Factors of 15:
- The factors of 15 are the numbers that divide 15 evenly. They are: 1, 3, 5, and 15.

2. Multiples of 3:
- A number is a multiple of 3 if it can be expressed as \( 3 \times k \), where \( k \) is an integer.

Now, let's fill in the table for each number:

- Number: 3
- Factor of 15?: Yes (since 3 divides 15 evenly).
- Multiple of 3?: Yes (since \( 3 = 3 \times 1 \)).

- Number: 30
- Factor of 15?: No (since 30 does not divide 15 evenly).
- Multiple of 3?: Yes (since \( 30 = 3 \times 10 \)).

- Number: 6
- Factor of 15?: No (since 6 does not divide 15 evenly).
- Multiple of 3?: Yes (since \( 6 = 3 \times 2 \)).

- Number: 12
- Factor of 15?: No (since 12 does not divide 15 evenly).
- Multiple of 3?: Yes (since \( 12 = 3 \times 4 \)).

- Number: 20
- Factor of 15?: No (since 20 does not divide 15 evenly).
- Multiple of 3?: No (since 20 is not divisible by 3).

#### Final Table:
| NUMBER | FACTOR OF 15? | MULTIPLES OF 3? |
|--------|---------------|------------------|
| 3 | Yes | Yes |
| 30 | No | Yes |
| 6 | No | Yes |
| 12 | No | Yes |
| 20 | No | No |

---

Task 2: Complete the factor tree

#### Factor Tree for 60:
1. Start with 60.
2. Break it down into two factors: \( 60 = 30 \times 2 \).
3. Break down 30 further: \( 30 = 10 \times 3 \).
4. Break down 10 further: \( 10 = 5 \times 2 \).

So, the complete factor tree for 60 is:
```
60
/ \
30 2
/ \
10 3
/ \
5 2
```

#### Factor Tree for 48:
1. Start with 48.
2. Break it down into two factors: \( 48 = 4 \times 12 \).
3. Break down 4 further: \( 4 = 2 \times 2 \).
4. Break down 12 further: \( 12 = 3 \times 4 \).
5. Break down 4 again: \( 4 = 2 \times 2 \).

So, the complete factor tree for 48 is:
```
48
/ \
4 12
/ \ / \
2 2 3 4
/ \
2 2
```

#### Final Factor Trees:
- For 60:
```
60
/ \
30 2
/ \
10 3
/ \
5 2
```

- For 48:
```
48
/ \
4 12
/ \ / \
2 2 3 4
/ \
2 2
```

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Task 3: I am a multiple of 60. I am between 400 and 600. I am 40 away from a multiple of 100. Who am I?

#### Step-by-Step Solution:
1. Identify multiples of 60 between 400 and 600:
- The multiples of 60 are: \( 60 \times 7 = 420 \), \( 60 \times 8 = 480 \), \( 60 \times 9 = 540 \), \( 60 \times 10 = 600 \).
- Between 400 and 600, the multiples are: 420, 480, 540.

2. Check which of these is 40 away from a multiple of 100:
- 420: Closest multiples of 100 are 400 and 500.
- Distance from 400: \( 420 - 400 = 20 \) (not 40).
- Distance from 500: \( 500 - 420 = 80 \) (not 40).
- 480: Closest multiples of 100 are 400 and 500.
- Distance from 400: \( 480 - 400 = 80 \) (not 40).
- Distance from 500: \( 500 - 480 = 20 \) (not 40).
- 540: Closest multiples of 100 are 500 and 600.
- Distance from 500: \( 540 - 500 = 40 \) (matches the condition).
- Distance from 600: \( 600 - 540 = 60 \) (not 40).

3. Conclusion:
- The number that satisfies both conditions is 540.

#### Final Answer:
\[
\boxed{540}
\]

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Final Summary of Answers:

1. Table:
| NUMBER | FACTOR OF 15? | MULTIPLES OF 3? |
|--------|---------------|------------------|
| 3 | Yes | Yes |
| 30 | No | Yes |
| 6 | No | Yes |
| 12 | No | Yes |
| 20 | No | No |

2. Factor Trees:
- For 60:
```
60
/ \
30 2
/ \
10 3
/ \
5 2
```
- For 48:
```
48
/ \
4 12
/ \ / \
2 2 3 4
/ \
2 2
```

3. Who am I?:
\[
\boxed{540}
\]