Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Find the prime factorization of 256.

Sagot :

GinnyAnswer
To find the prime factorization of the number 256, you need to express 256 as a product of prime numbers. Let's follow these steps to achieve that:

1. Start by dividing the number by the smallest prime number, which is 2.
2. Determine how many times 2 divides into 256 completely.

- 256 ÷ 2 = 128
- 128 ÷ 2 = 64
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1

3. After continuously dividing by 2, we finally reach 1, which means no further division is possible by 2.

By examining the results of each division, we see that 256 can be divided by 2 exactly 8 times. Therefore, we express 256 as:

[tex]\[ 256 = 2^8 \][/tex]

Thus, the prime factorization of 256 is:

[tex]\[ 256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \][/tex]

Or more compactly:

[tex]\[ 256 = 2^8 \][/tex]

So the prime factorization of 256 is [tex]\( 2^8 \)[/tex].
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.