Use a factor tree to write 256 as the product of its-prime factors.

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UpStudy AI · Accepted Answer

To express 256 as the product of its prime factors using a factor tree, we can follow these steps:

1. **Start with the number 256.**
2. **Divide it by the smallest prime number (2) until you can no longer divide evenly.**
3. **Continue dividing the resulting quotient by the smallest prime number until you reach 1.**

Let's break it down step by step:

- Start with 256.
- Divide by 2: 
  - $$ 256 \div 2 = 128 $$
- Divide 128 by 2:
  - $$ 128 \div 2 = 64 $$
- Divide 64 by 2:
  - $$ 64 \div 2 = 32 $$
- Divide 32 by 2:
  - $$ 32 \div 2 = 16 $$
- Divide 16 by 2:
  - $$ 16 \div 2 = 8 $$
- Divide 8 by 2:
  - $$ 8 \div 2 = 4 $$
- Divide 4 by 2:
  - $$ 4 \div 2 = 2 $$
- Finally, divide 2 by 2:
  - $$ 2 \div 2 = 1 $$

Now, we can summarize the divisions:

- $$ 256 = 2 \times 128 $$
- $$ 128 = 2 \times 64 $$
- $$ 64 = 2 \times 32 $$
- $$ 32 = 2 \times 16 $$
- $$ 16 = 2 \times 8 $$
- $$ 8 = 2 \times 4 $$
- $$ 4 = 2 \times 2 $$

Thus, we can express 256 as:

$$
256 = 2^8
$$

So, the prime factorization of 256 is $$ 2^8 $$.
256 can be expressed as $$ 2^8 $$ using a factor tree.

Use a factor tree to write 256 as
the product of its-prime factors.

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