Find the prime factorisation of the numbers:
320

Options

A. `2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 5`
B. `2 xx 2 xx 2 xx 2 xx xx 2 xx 5`
C. `2 xx 2 xx 2 xx 2 xx 2 xx 3 xx 5`
D. `2 xx 2 xx 2 xx 3 xx 3 xx 2 xx 5`

Answer

To find the prime factorization of the number 320, we can use the method of factorization. Here’s a step-by-step solution:

### Step 1: Start with the number 320
We begin with the number 320.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2. We check if 320 is divisible by 2.
- \( 320 \div 2 = 160 \)

### Step 3: Continue dividing by 2
Now we take the quotient (160) and divide it by 2 again.
- \( 160 \div 2 = 80 \)

### Step 4: Keep dividing by 2
We continue this process:
- \( 80 \div 2 = 40 \)
- \( 40 \div 2 = 20 \)
- \( 20 \div 2 = 10 \)
- \( 10 \div 2 = 5 \)

### Step 5: Stop when you reach a prime number
Now we have reached 5, which is a prime number. We cannot divide 5 by 2 anymore, so we stop here.

### Step 6: Write the prime factorization
Now we can write the prime factorization of 320 as:
- \( 320 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \)
- This can also be written in exponential form as:
- \( 320 = 2^5 \times 5^1 \)

### Final Answer
Thus, the prime factorization of 320 is:
- \( 320 = 2^5 \times 5^1 \)

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