Find the prime factorisation of 112 using the factor tree

Answer

To find the prime factorization of 112 using a factor tree, we will follow these steps:

### Step 1: Start with the number
We begin with the number 112.

### Step 2: Find the first prime factor
The smallest prime number is 2. We check if 112 is divisible by 2. Since 112 is an even number, it is divisible by 2.

**Calculation:**
112 ÷ 2 = 56

### Step 3: Continue factoring
Next, we take 56 and check if it can be divided by 2 again.

**Calculation:**
56 ÷ 2 = 28

### Step 4: Keep factoring
Now we take 28 and divide it by 2.

**Calculation:**
28 ÷ 2 = 14

### Step 5: Factor again
Next, we take 14 and divide it by 2.

**Calculation:**
14 ÷ 2 = 7

### Step 6: Identify the last factor
Now we have reached 7. Since 7 is a prime number, we cannot factor it any further.

### Step 7: Write the prime factorization
Now we can write the prime factorization of 112. We have divided by 2 four times and ended with 7.

**Final Prime Factorization:**
112 = 2 × 2 × 2 × 2 × 7
or in exponential form,
112 = 2^4 × 7

### Summary of the Prime Factorization
Thus, the prime factorization of 112 is \( 2^4 \times 7 \).

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