Find the prime factorisation of:
252

Answer

To find the prime factorization of 252, we will divide the number by the smallest prime numbers until we reach 1. Here’s the step-by-step solution:

### Step 1: Divide by the smallest prime number
- Start with 252. The smallest prime number is 2.
- **Calculation**: 252 ÷ 2 = 126

### Step 2: Continue dividing by 2
- Now take 126 and divide it by 2 again.
- **Calculation**: 126 ÷ 2 = 63

### Step 3: Move to the next smallest prime number
- Since 63 is not divisible by 2, we move to the next prime number, which is 3.
- **Calculation**: 63 ÷ 3 = 21

### Step 4: Continue dividing by 3
- Now take 21 and divide it by 3 again.
- **Calculation**: 21 ÷ 3 = 7

### Step 5: Divide by the next prime number
- Now we have 7, which is a prime number itself.
- **Calculation**: 7 ÷ 7 = 1

### Step 6: Write down the prime factors
- We have divided 252 down to 1, and the prime factors we used are:
- 2 (used twice)
- 3 (used twice)
- 7 (used once)

### Final Step: Express the prime factorization
- We can express the prime factorization of 252 as:
- \( 2^2 \times 3^2 \times 7^1 \)

Thus, the prime factorization of 252 is \( 2^2 \times 3^2 \times 7^1 \).

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