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Chapter 1: Problem 25

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$81$$

Short Answer

Expert verified
The number 81 is a composite number. Its prime factorization is \(81 = 3^4\).

Step by step solution

01

Identify the Number as Prime or Composite

To find if the number 81 is prime or composite, check if the number has any other divisors apart from 1 and itself. In this case, 81 can be divided evenly by other numbers, such as 3 and 27, so it is identified as a composite number.
02

Find the Prime Factorization

To find the prime factorization of 81, we should divide the number by prime numbers, starting from the smallest (2), and continue until the result is a prime number. However, 81 is odd, so it can't be divided by 2. So, moving on to the next smallest prime number, 3, 81 is divided by 3 to give 27. Again, 27 can be divided by 3 to give 9, and subsequently 9 divided by 3 gives 3. So, \(81 = 3 脳 3 脳 3 脳 3\), or, in general terms, also known as \(81 = 3^4\). Here, we see that 4 is the power of the prime number 3, indicates that 3 is used 4 times to multiply to get the composite number 81.

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