Grade IV math worksheet focusing on multiples and factors, including exercises on writing multiples, identifying multiples, finding common multiples, LCM, factors, and HCF.

Let's solve each question step by step from the worksheet titled "Multiples And Factors" for Grade IV.

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1. Write the first five multiples of the following.

a. 4
Multiples of 4:
4 × 1 = 4
4 × 2 = 8
4 × 3 = 12
4 × 4 = 16
4 × 5 = 20

✔ Answer: 4, 8, 12, 16, 20

b. 11
Multiples of 11:
11 × 1 = 11
11 × 2 = 22
11 × 3 = 33
11 × 4 = 44
11 × 5 = 55

✔ Answer: 11, 22, 33, 44, 55

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2. Answer the following in Yes or No.

a. Is 112 a multiple of 4?
Divide 112 ÷ 4 = 28 → No remainder
✔ Answer: Yes

b. Is 1586 a multiple of 15?
Check divisibility:
- A number is divisible by 15 if it is divisible by both 3 and 5.
- For 5: last digit must be 0 or 5 → 1586 ends in 6 → Not divisible by 5
→ So not divisible by 15

✔ Answer: No

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3. Find four common multiples of the following.

a. 4 and 5
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60,...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,...

Common multiples: 20, 40, 60, 80,...

✔ Answer: 20, 40, 60, 80

b. 3 and 6
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...
Multiples of 6: 6, 12, 18, 24, 30, 36,...

Common multiples: 6, 12, 18, 24,...

✔ Answer: 6, 12, 18, 24

c. 5 and 10
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40,...
Multiples of 10: 10, 20, 30, 40, 50,...

Common multiples: 10, 20, 30, 40,...

✔ Answer: 10, 20, 30, 40

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4. Find the LCM of the following.

LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers.

a. 6 and 8
List multiples:
- 6: 6, 12, 18, 24, 30, ...
- 8: 8, 16, 24, 32, ...

First common multiple: 24

✔ Answer: 24

b. 5 and 7
5: 5, 10, 15, 20, 25, 30, 35, ...
7: 7, 14, 21, 28, 35, ...

First common multiple: 35

✔ Answer: 35

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5. Find the factors of the following number using multiplication method.

a. 25
We find pairs of numbers that multiply to give 25:

- 1 × 25 = 25
- 5 × 5 = 25

So the factors are: 1, 5, 25

✔ Answer: 1, 5, 25

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6. Find the factors of the following number using division method.

a. 72
We divide 72 by numbers starting from 1 and check if they divide evenly.

| Divisor | Division | Result |
|--------|----------|--------|
| 1 | 72 ÷ 1 | 72 → yes → factor: 1, 72 |
| 2 | 72 ÷ 2 | 36 → yes → factor: 2, 36 |
| 3 | 72 ÷ 3 | 24 → yes → factor: 3, 24 |
| 4 | 72 ÷ 4 | 18 → yes → factor: 4, 18 |
| 6 | 72 ÷ 6 | 12 → yes → factor: 6, 12 |
| 8 | 72 ÷ 8 | 9 → yes → factor: 8, 9 |
| 9 | already have |
| 12 | already have |

Now list all unique factors:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

✔ Answer: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

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7. Find the HCF of the following.

HCF (Highest Common Factor) is the largest number that divides both numbers.

a. 8 and 12

Find factors:

- Factors of 8: 1, 2, 4, 8
- Factors of 12: 1, 2, 3, 4, 6, 12

Common factors: 1, 2, 4
Largest: 4

✔ Answer: 4

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✔ Final Answers Summary:

#### 1.
a. 4, 8, 12, 16, 20
b. 11, 22, 33, 44, 55

#### 2.
a. Yes
b. No

#### 3.
a. 20, 40, 60, 80
b. 6, 12, 18, 24
c. 10, 20, 30, 40

#### 4.
a. 24
b. 35

#### 5.
a. 1, 5, 25

#### 6.
a. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

#### 7.
a. 4

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