Question

Write the prime factorization. (Skills Review, p. \(T T T\) ) $$24$$

Short answer

The prime factorization of 24 is \(2^3 * 3\).

Step-by-step solution

Find the First Pair of Factors

First, identify a pair of factors for 24. You can start with the number 1 and the number itself (24). However, since 24 isn't a prime number, this step is typically bypassed in favor of finding two factors where one of them is a prime number. A pair of factors of 24 include 2 and 12, so you can write 24 as 2*12.

Break Down Composite Factors

Continuing the factor tree, identify factors of 12. Since 12 isn't a prime number, find a pair of factors where one of them is a prime number. A pair of factors could be 2 and 6. Write 12 as 2*6 to continue the factor tree.

Continue Until All Factors are Prime

The number 6 is a composite number, and it can be written as a product of two primes, 2 and 3. Now, the number 2 and 3 are prime numbers and cannot be factored any further.

Write the Prime Factorization

Put all the prime numbers you identified together to write the prime factorization of 24. So, 24 can be written as the product of these prime numbers: \(2^3 * 3\).