The prime factorisation of 640 is:

Options

A. `2 xx 2 xx 2 xx 2 xx 2 xx5`
B. `2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 5`
C. `2 xx 2xx2 xx2xx2 xx 5 xx5`
D. `2 xx 2 xx 2 xx2 xx 2 xx 2 xx 2 xx5`

Answer

To find the prime factorization of 640, we can follow these steps:

### Step-by-Step Solution:

1. **Start with the number**: We begin with the number 640.

2. **Divide by the smallest prime number**: The smallest prime number is 2. We check if 2 divides 640:
\[ 640 \div 2 = 320 \]
So, we can write:
\[ 640 = 2 \times 320 \]

3. **Repeat the process**: Now we take 320 and divide it by 2 again:
\[ 320 \div 2 = 160 \]
Thus, we can write:
\[ 640 = 2 \times 2 \times 160 \]

4. **Continue dividing by 2**: Next, we take 160 and divide it by 2:
\[ 160 \div 2 = 80 \]
So, we have:
\[ 640 = 2 \times 2 \times 2 \times 80 \]

5. **Keep dividing by 2**: Now we take 80 and divide it by 2:
\[ 80 \div 2 = 40 \]
This gives us:
\[ 640 = 2 \times 2 \times 2 \times 2 \times 40 \]

6. **Continue the division**: Next, we divide 40 by 2:
\[ 40 \div 2 = 20 \]
So we have:
\[ 640 = 2 \times 2 \times 2 \times 2 \times 2 \times 20 \]

7. **Divide 20 by 2**: Now we take 20 and divide it by 2:
\[ 20 \div 2 = 10 \]
Thus, we can write:
\[ 640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 10 \]

8. **Finally, divide 10 by 2**: Lastly, we divide 10 by 2:
\[ 10 \div 2 = 5 \]
Therefore, we have:
\[ 640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \]

9. **Count the factors**: We can count how many times we used 2:
- We used 2 a total of 7 times, and we have one 5.
- Thus, we can express this as:
\[ 640 = 2^7 \times 5^1 \]

### Final Answer:
The prime factorization of 640 is:
\[ 2^7 \times 5 \]