Math worksheet focusing on factors and multiples, featuring eight questions that test understanding of factor, multiple, and neither classifications, with examples and number lists.

Let's solve each question step by step and explain the reasoning.

---

#1

F = factor, M = multiple, B = both a factor and a multiple, N = neither.
What letter describes each number below for the number "12"?
Numbers: 6, 24, 5, 9, 36

We are analyzing whether each number is a factor, multiple, both, or neither of 12.

- 6:
- Is 6 a factor of 12? Yes (12 ÷ 6 = 2) → F
- Is 6 a multiple of 12? No (12 × 0.5 = 6, but multiples must be whole number results) → Not a multiple
→ F

- 24:
- Is 24 a factor of 12? No (12 ÷ 24 = 0.5) → Not a factor
- Is 24 a multiple of 12? Yes (12 × 2 = 24) → M
→ M

- 5:
- Is 5 a factor of 12? No (12 ÷ 5 = 2.4) → Not a factor
- Is 5 a multiple of 12? No (12 × 0.416… = 5) → Not a multiple
→ N

- 9:
- Is 9 a factor of 12? No (12 ÷ 9 ≈ 1.33) → Not a factor
- Is 9 a multiple of 12? No → Not a multiple
→ N

- 36:
- Is 36 a factor of 12? No (36 > 12, can't divide evenly) → Not a factor
- Is 36 a multiple of 12? Yes (12 × 3 = 36) → M
→ M

✔ Answer #1:
6 → F
24 → M
5 → N
9 → N
36 → M

---

#2

What numbers inside the box are factors of the number outside the box?
Outside: 15
Inside: 15, 1, 30, 2, 25, 45, 5, 10

We check which numbers in the list divide 15 evenly.

- 15 ÷ 15 = 1 → yes → 15
- 15 ÷ 1 = 15 → yes → 1
- 15 ÷ 30 = 0.5 → no
- 15 ÷ 2 = 7.5 → no
- 15 ÷ 25 = 0.6 → no
- 15 ÷ 45 = 0.333… → no
- 15 ÷ 5 = 3 → yes → 5
- 15 ÷ 10 = 1.5 → no

✔ Answer #2: Factors of 15 from the list: 15, 1, 5

---

#3

Write all the factors of 30 (there are eight of them)

Find all numbers that divide 30 evenly:

- 1 × 30 = 30
- 2 × 15 = 30
- 3 × 10 = 30
- 5 × 6 = 30

So the factors are: 1, 2, 3, 5, 6, 10, 15, 30

✔ Answer #3: 1, 2, 3, 5, 6, 10, 15, 30

---

#4

This block has three multiples in it. Write the next four multiples that follow.
Given: 28, 35, 42

Look at the pattern:
- 28 → 35 → +7
- 35 → 42 → +7

So the common difference is 7 → these are multiples of 7.

Next four multiples:
- 42 + 7 = 49
- 49 + 7 = 56
- 56 + 7 = 63
- 63 + 7 = 70

✔ Answer #4: 49, 56, 63, 70

---

#5

If you took the third factor of 24 and added it to the last factor of 16, what would you end up with?

First, find factors of 24 in order:
- 1, 2, 3, 4, 6, 8, 12, 24 → so the third factor is 3

Now, factors of 16:
- 1, 2, 4, 8, 16 → the last factor is 16

Add: 3 + 16 = 19

✔ Answer #5: 19

---

#6

The last factor of 30 and the first multiple of 30 is the same number — what is it?

- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 → last factor = 30
- Multiples of 30: 30, 60, 90, ... → first multiple = 30

So both are 30

✔ Answer #6: 30

---

#7

Write the multiples of 8 that are greater than 30 but less than 67

Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, ...

Now pick those between 30 and 67:
- 32 (yes)
- 40 (yes)
- 48 (yes)
- 56 (yes)
- 64 (yes)
- 72 > 67 → stop

✔ Answer #7: 32, 40, 48, 56, 64

---

#8

F = factor, M = multiple, B = both, N = neither
What letter describes each number below for the number "8"?
Numbers: 26, 18, 32, 4, 16

Check each:

- 26:
- Factor of 8? 8 ÷ 26 = no → not a factor
- Multiple of 8? 8 × 3 = 24, 8 × 4 = 32 → 26 not a multiple → N

- 18:
- Factor of 8? 8 ÷ 18 = no → not a factor
- Multiple of 8? 8 × 2 = 16, 8 × 3 = 24 → 18 not a multiple → N

- 32:
- Factor of 8? 32 ÷ 8 = 4 → yes → F
But is 32 a multiple of 8? Yes (8 × 4 = 32) → So it’s both a factor and multiple? Wait — no.

Wait: Is 32 a factor of 8?
No! 8 ÷ 32 = 0.25 → not a factor.
But 32 is a multiple of 8 (8 × 4 = 32).
So:
- Factor of 8? No
- Multiple of 8? Yes → M

- 4:
- Factor of 8? 8 ÷ 4 = 2 → yes → F
- Multiple of 8? 8 × 0.5 = 4 → not a whole number multiple → not a multiple
→ F

- 16:
- Factor of 8? 8 ÷ 16 = 0.5 → no
- Multiple of 8? 8 × 2 = 16 → yes → M

✔ Answer #8:
26 → N
18 → N
32 → M
4 → F
16 → M

---

✔ Final Answers Summary:

1. 6 → F, 24 → M, 5 → N, 9 → N, 36 → M
2. Factors of 15: 15, 1, 5
3. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
4. Next four multiples: 49, 56, 63, 70
5. Third factor of 24 = 3; last factor of 16 = 16 → 3 + 16 = 19
6. Last factor of 30 = 30; first multiple of 30 = 30 → 30
7. Multiples of 8 between 30 and 67: 32, 40, 48, 56, 64
8. 26 → N, 18 → N, 32 → M, 4 → F, 16 → M

Let me know if you'd like this formatted as a printable answer sheet!