Find the prime factorisation of:
270

Answer

To find the prime factorization of 270, we will divide the number by the smallest prime numbers until we reach 1. Here are the steps:

### Step 1: Start with the number 270.
- We will check if 270 is divisible by the smallest prime number, which is 2.

### Step 2: Divide 270 by 2.
- \( 270 \div 2 = 135 \)
- So, we have \( 270 = 2 \times 135 \).

### Step 3: Now take the quotient 135 and divide it by the next smallest prime number, which is 3.
- \( 135 \div 3 = 45 \)
- Thus, we can write \( 135 = 3 \times 45 \).
- So far, we have \( 270 = 2 \times 3 \times 45 \).

### Step 4: Next, take 45 and divide it by 3 again.
- \( 45 \div 3 = 15 \)
- Therefore, \( 45 = 3 \times 15 \).
- Now we have \( 270 = 2 \times 3 \times 3 \times 15 \).

### Step 5: Now take 15 and divide it by 3 once more.
- \( 15 \div 3 = 5 \)
- So, \( 15 = 3 \times 5 \).
- Now we can write \( 270 = 2 \times 3 \times 3 \times 3 \times 5 \).

### Step 6: Finally, we have reached the last prime number, which is 5.
- \( 5 \div 5 = 1 \)
- This means we have fully factored 270.

### Step 7: Combine the prime factors.
- We can express the prime factorization as:
\[ 270 = 2^1 \times 3^3 \times 5^1 \]

### Final Answer:
The prime factorization of 270 is \( 2^1 \times 3^3 \times 5^1 \).

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