Keith identified the prime factors of 72 as 9 x 2 x 2 x 2 . Explain his error. Write the correct answer.
Can 9 also be factored?
Keith made an error in identifying the prime factors of 72. The prime factors of 72 are actually 2 x 2 x 2 x 3 x 3.
To find the prime factors of a number, we start by dividing the number by the smallest prime number, which is 2. We continue dividing the quotient by the smallest prime number until we can no longer divide evenly. Then, we move on to the next prime number and repeat the process until we reach 1.
In this case, we can start by dividing 72 by 2, which gives us a quotient of 36. We can divide 36 by 2 again, resulting in a quotient of 18. We can continue dividing 18 by 2 once more, which gives us a quotient of 9. At this point, we can't divide 9 by 2 anymore. So, we move on to the next prime number, which is 3.
Dividing 9 by 3 gives us a quotient of 3. Now, we can't divide 3 any further because it is a prime number itself. Therefore, the prime factors of 72 are 2 x 2 x 2 x 3 x 3.
So, the correct answer is that the prime factors of 72 are 2 x 2 x 2 x 3 x 3.