Question

In the context of Big Ideas Math homework 1.3, complete the sentence:

The prime factorization of ____ is ____.

Answer 1

The prime factorization of 24 is accomplished by dividing by the number's smallest prime factors until reaching 1. For 24, it is divided by 2 three times and then by 3 once, resulting in the prime factorization of 2³ × 3.

Step-by-step explanation:

The prime factorization of a number is breaking it down into the product of its prime factors. Prime numbers are the building blocks of all natural numbers and play a crucial role in various mathematical concepts, including prime factorization. Let's say we want to find the prime factorization of 24. Following a step-by-step approach:

1. First, we divide 24 by the smallest prime number it is divisible by, which is 2. The result is 24 ÷ 2 = 12.
2. Then, we divide 12 by 2 again to get 6.
3. Continuing in this fashion, we divide 6 by 2 to get 3.
4. Finally, we divide 3 by itself, since 3 is a prime number, we are left with 1. At this point, the process ends because 1 is not further divisible by any prime number.

So, we divided 24 by 2 three times and then by 3 once. Therefore, the prime factorization of 24 is 2³ × 3.

To complete the sentence we would say: The prime factorization of 24 is 2³ × 3.