Find the prime factorisation of the following numbers:
450

Answer

To find the prime factorization of the number 450, we will break it down into its prime factors step by step.

### Step 1: Start with the number 450
We begin with the number 450.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2. We check if 450 is divisible by 2:
- 450 ÷ 2 = 225
Since 450 is even, it is divisible by 2.

### Step 3: Continue with the quotient
Now we take the quotient 225 and check for divisibility by the next smallest prime number, which is 3:
- 225 ÷ 3 = 75
225 is divisible by 3.

### Step 4: Repeat the process
Next, we take 75 and check for divisibility by 3 again:
- 75 ÷ 3 = 25
75 is also divisible by 3.

### Step 5: Move to the next prime number
Now we take 25 and check for divisibility by the next smallest prime number, which is 5:
- 25 ÷ 5 = 5
25 is divisible by 5.

### Step 6: Final division
Now we take 5 and divide it by itself:
- 5 ÷ 5 = 1
We have reached 1, which means we can stop here.

### Step 7: Write down the prime factors
Now we can write down the prime factors we found:
- From our divisions, we have:
- 2 (from the first step)
- 3 (from the second and third steps, counted twice)
- 5 (from the fourth and fifth steps, counted twice)

### Step 8: Express in exponential form
The prime factorization of 450 can be expressed as:
- \( 450 = 2^1 \times 3^2 \times 5^2 \)

### Final Answer:
The prime factorization of 450 is \( 2^1 \times 3^2 \times 5^2 \).

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