Math worksheet focusing on factors and multiples, designed for educational practice with interactive exercises.

Let's solve this step-by-step, explaining each part clearly.

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Section A

#### Question 1:
We are given a part of a 100 square:

```
12 | 13 | 14 | 15
-----|----|----|----
22 | 23 | 24 | 25
-----|----|----|----
32 | 33 | 34 | 35
-----|----|----|----
42 | 43 | 44 | 45
```

- Shaded numbers: 12, 15, 24, 33, 42, 45
(These are in yellow)

- Circled numbers: 12, 24, 32, 44

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What do the shaded numbers have in common?

Let’s look at the shaded numbers:
- 12, 15, 24, 33, 42, 45

Check if they are multiples of any number:
- 12 = 3×4 → divisible by 3
- 15 = 3×5 → divisible by 3
- 24 = 3×8 → divisible by 3
- 33 = 3×11 → divisible by 3
- 42 = 3×14 → divisible by 3
- 45 = 3×15 → divisible by 3

✔ All shaded numbers are multiples of 3.

> ✔ Answer: These numbers are all multiples of 3.

---

What do the circled numbers have in common?

Circled numbers: 12, 24, 32, 44

Check them:
- 12 → even
- 24 → even
- 32 → even
- 44 → even

All are even numbers (divisible by 2).

But let's check for more patterns.

Look at their digits:
- 12: ends in 2
- 24: ends in 4
- 32: ends in 2
- 44: ends in 4

They all end in even digits, but that’s just because they're even.

Wait — look at the positions on the grid. Notice:
- 12 → row 1, column 1
- 24 → row 2, column 3
- 32 → row 3, column 1
- 44 → row 4, column 3

Not obvious.

But observe:
12, 24, 32, 44 — all are even, but is there a better pattern?

Try dividing by 4:
- 12 ÷ 4 = 3 → yes
- 24 ÷ 4 = 6 → yes
- 32 ÷ 4 = 8 → yes
- 44 ÷ 4 = 11 → yes

✔ All are multiples of 4!

Wait — 12, 24, 32, 44 — are they all divisible by 4?

Yes:
- 12 ÷ 4 = 3 ✔️
- 24 ÷ 4 = 6 ✔️
- 32 ÷ 4 = 8 ✔️
- 44 ÷ 4 = 11 ✔️

So, all are multiples of 4.

> ✔ Answer: These numbers are all multiples of 4.

---

#### Question 2:

Another part of the 100 square:

```
55 | 56 | 57 | 58 | 59 | 60
----|----|----|----|----|----
65 | 66 | 67 | 68 | 69 | 70
----|----|----|----|----|----
75 | 76 | 77 | 78 | 79 | 80
----|----|----|----|----|----
85 | 86 | 87 | 88 | 89 | 90
```

- Shaded numbers: 55, 60, 70, 80, 90, and also 65, 75, 85 — wait, let's list carefully.

From the image:
- Yellow shaded: 55, 60, 65, 70, 75, 80, 85, 90

So shaded: 55, 60, 65, 70, 75, 80, 85, 90

Look at these:
- All end in 0 or 5 → they are multiples of 5

Check:
- 55 = 5×11
- 60 = 5×12
- 65 = 5×13
- 70 = 5×14
- 75 = 5×15
- 80 = 5×16
- 85 = 5×17
- 90 = 5×18

✔ All are multiples of 5.

> ✔ Answer: These numbers are all multiples of 5.

---

Circled numbers: 55, 66, 77, 88

List: 55, 66, 77, 88

Check:
- 55 = 5×11
- 66 = 6×11
- 77 = 7×11
- 88 = 8×11

All are multiples of 11!

Also, notice:
- 55 → 5×11
- 66 → 6×11
- 77 → 7×11
- 88 → 8×11

So they are multiples of 11.

> ✔ Answer: These numbers are all multiples of 11.

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Section B: Complete the sentences

We’re to fill in the blanks using terms like factor, multiple, common factor, common multiple, etc.

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Example:
3 is a factor of 9; 9 is a multiple of 3.

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1) 18 is a _________ of 3; 3 is a _________ of 18.

- 18 ÷ 3 = 6 → so 18 is a multiple of 3
- 3 × 6 = 18 → so 3 is a factor of 18

✔ Answer:
18 is a multiple of 3; 3 is a factor of 18.

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2) 4 and 5 are common _________ of 20; 20 is a _________ of 4 and 5.

- 4 divides 20 → 4 is a factor of 20
- 5 divides 20 → 5 is a factor of 20
- So 4 and 5 are common factors of 20
- 20 is a multiple of both 4 and 5

✔ Answer:
4 and 5 are common factors of 20; 20 is a multiple of 4 and 5.

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3) The highest common _________ of 18 and 30 is 6.

- HCF (Highest Common Factor) of 18 and 30 is 6

✔ Answer: factor

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4) 12 is a _________ of 24; 24 is a _________ of 12.

- 12 × 2 = 24 → so 12 is a factor of 24
- 24 ÷ 12 = 2 → so 24 is a multiple of 12

✔ Answer:
12 is a factor of 24; 24 is a multiple of 12.

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5) The lowest common _________ of 4 and 10 is 20.

- LCM (Lowest Common Multiple) of 4 and 10 is 20

✔ Answer: multiple

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6) 1 is a _________ of every number.

- Every number divided by 1 gives itself → 1 is a factor of every number

✔ Answer: factor

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7) 0 is a _________ of every number.

- Is 0 a factor of every number? No! You can’t divide by 0.
- But: Any number × 0 = 0 → so 0 is a multiple of every number.

For example:
- 5 × 0 = 0 → 0 is a multiple of 5
- 10 × 0 = 0 → 0 is a multiple of 10

So, 0 is a multiple of every number

✔ Answer: multiple

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✔ Final Answers:

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Section A

1)
- Shaded numbers: Multiples of 3
- Circled numbers: Multiples of 4

2)
- Shaded numbers: Multiples of 5
- Circled numbers: Multiples of 11

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Section B

1) 18 is a multiple of 3; 3 is a factor of 18.
2) 4 and 5 are common factors of 20; 20 is a multiple of 4 and 5.
3) The highest common factor of 18 and 30 is 6.
4) 12 is a factor of 24; 24 is a multiple of 12.
5) The lowest common multiple of 4 and 10 is 20.
6) 1 is a factor of every number.
7) 0 is a multiple of every number.

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