Write down all the factors of
(i) 20, (ii) 36, (iii) 60 (iv) 75

Answer

To find the factors of the given numbers, we need to identify all the integers that can divide each number without leaving a remainder. Let's go through each number step by step.

### Step-by-Step Solution:

**(i) Factors of 20:**
1. Start with 1: \(20 \div 1 = 20\) (remainder 0) → factor is 1.
2. Next, try 2: \(20 \div 2 = 10\) (remainder 0) → factor is 2.
3. Try 3: \(20 \div 3 = 6.67\) (not a whole number) → not a factor.
4. Try 4: \(20 \div 4 = 5\) (remainder 0) → factor is 4.
5. Try 5: \(20 \div 5 = 4\) (remainder 0) → factor is 5.
6. Try 6: \(20 \div 6 = 3.33\) (not a whole number) → not a factor.
7. Try 10: \(20 \div 10 = 2\) (remainder 0) → factor is 10.
8. Finally, try 20: \(20 \div 20 = 1\) (remainder 0) → factor is 20.

**Factors of 20:** 1, 2, 4, 5, 10, 20.

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**(ii) Factors of 36:**
1. Start with 1: \(36 \div 1 = 36\) (remainder 0) → factor is 1.
2. Next, try 2: \(36 \div 2 = 18\) (remainder 0) → factor is 2.
3. Try 3: \(36 \div 3 = 12\) (remainder 0) → factor is 3.
4. Try 4: \(36 \div 4 = 9\) (remainder 0) → factor is 4.
5. Try 5: \(36 \div 5 = 7.2\) (not a whole number) → not a factor.
6. Try 6: \(36 \div 6 = 6\) (remainder 0) → factor is 6.
7. Try 9: \(36 \div 9 = 4\) (remainder 0) → factor is 9.
8. Try 12: \(36 \div 12 = 3\) (remainder 0) → factor is 12.
9. Finally, try 18: \(36 \div 18 = 2\) (remainder 0) → factor is 18.
10. Lastly, try 36: \(36 \div 36 = 1\) (remainder 0) → factor is 36.

**Factors of 36:** 1, 2, 3, 4, 6, 9, 12, 18, 36.

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**(iii) Factors of 60:**
1. Start with 1: \(60 \div 1 = 60\) (remainder 0) → factor is 1.
2. Next, try 2: \(60 \div 2 = 30\) (remainder 0) → factor is 2.
3. Try 3: \(60 \div 3 = 20\) (remainder 0) → factor is 3.
4. Try 4: \(60 \div 4 = 15\) (remainder 0) → factor is 4.
5. Try 5: \(60 \div 5 = 12\) (remainder 0) → factor is 5.
6. Try 6: \(60 \div 6 = 10\) (remainder 0) → factor is 6.
7. Try 10: \(60 \div 10 = 6\) (remainder 0) → factor is 10.
8. Try 12: \(60 \div 12 = 5\) (remainder 0) → factor is 12.
9. Try 15: \(60 \div 15 = 4\) (remainder 0) → factor is 15.
10. Try 20: \(60 \div 20 = 3\) (remainder 0) → factor is 20.
11. Try 30: \(60 \div 30 = 2\) (remainder 0) → factor is 30.
12. Finally, try 60: \(60 \div 60 = 1\) (remainder 0) → factor is 60.

**Factors of 60:** 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

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**(iv) Factors of 75:**
1. Start with 1: \(75 \div 1 = 75\) (remainder 0) → factor is 1.
2. Next, try 2: \(75 \div 2 = 37.5\) (not a whole number) → not a factor.
3. Try 3: \(75 \div 3 = 25\) (remainder 0) → factor is 3.
4. Try 4: \(75 \div 4 = 18.75\) (not a whole number) → not a factor.
5. Try 5: \(75 \div 5 = 15\) (remainder 0) → factor is 5.
6. Try 6: \(75 \div 6 = 12.5\) (not a whole number) → not a factor.
7. Try 7: \(75 \div 7 = 10.71\) (not a whole number) → not a factor.
8. Try 8: \(75 \div 8 = 9.375\) (not a whole number) → not a factor.
9. Try 9: \(75 \div 9 = 8.33\) (not a whole number) → not a factor.
10. Try 15: \(75 \div 15 = 5\) (remainder 0) → factor is 15.
11. Finally, try 75: \(75 \div 75 = 1\) (remainder 0) → factor is 75.

**Factors of 75:** 1, 3, 5, 15, 25, 75.

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### Summary of Factors:
- **Factors of 20:** 1, 2, 4, 5, 10, 20
- **Factors of 36:** 1, 2, 3, 4, 6, 9, 12, 18, 36
- **Factors of 60:** 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- **Factors of 75:** 1, 3, 5, 15, 25, 75