List out all the common factors of the following pairs of numbers.
(a) 120 and 160 (b)52 and 32

Explanation

To find the common factors of the given pairs of numbers, we will follow these steps:

### Step 1: Find the factors of 120
To find the factors of 120, we can divide it by numbers starting from 1 up to 120 and check which numbers divide it evenly.

- 120 ÷ 1 = 120
- 120 ÷ 2 = 60
- 120 ÷ 3 = 40
- 120 ÷ 4 = 30
- 120 ÷ 5 = 24
- 120 ÷ 6 = 20
- 120 ÷ 8 = 15
- 120 ÷ 10 = 12

So, the factors of 120 are: **1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.**

### Step 2: Find the factors of 160
Now, let's find the factors of 160 in a similar way.

- 160 ÷ 1 = 160
- 160 ÷ 2 = 80
- 160 ÷ 4 = 40
- 160 ÷ 5 = 32
- 160 ÷ 8 = 20
- 160 ÷ 10 = 16

So, the factors of 160 are: **1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160.**

### Step 3: Identify the common factors of 120 and 160
Now, we will compare the factors of both numbers to find the common factors.

- Factors of 120: **1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120**
- Factors of 160: **1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160**

**Common factors are: 1, 2, 4, 5, 8, 10, 20, 40.**

### Step 4: Find the factors of 52
Next, we will find the factors of 52.

- 52 ÷ 1 = 52
- 52 ÷ 2 = 26
- 52 ÷ 4 = 13

So, the factors of 52 are: **1, 2, 4, 13, 26, 52.**

### Step 5: Find the factors of 32
Now, let's find the factors of 32.

- 32 ÷ 1 = 32
- 32 ÷ 2 = 16
- 32 ÷ 4 = 8

So, the factors of 32 are: **1, 2, 4, 8, 16, 32.**

### Step 6: Identify the common factors of 52 and 32
Now, we will compare the factors of both numbers to find the common factors.

- Factors of 52: **1, 2, 4, 13, 26, 52**
- Factors of 32: **1, 2, 4, 8, 16, 32**

**Common factors are: 1, 2, 4.**

### Final Answers:
(a) The common factors of 120 and 160 are: **1, 2, 4, 5, 8, 10, 20, 40.**

(b) The common factors of 52 and 32 are: **1, 2, 4.**

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