# Prime factorization of 32

#### Understand the Problem

The question is asking for the prime factorization of the number 32, which involves breaking down the number into its prime components. The process includes finding the prime numbers that multiply together to result in 32.

$2^5$

The final answer is $2^5$

#### Steps to Solve

1. Divide the number by the smallest prime number

Start by dividing 32 by the smallest prime number, which is 2.

$$32 \div 2 = 16$$

So, 32 can be written as $32 = 2 imes 16$

1. Continue dividing by the smallest prime number

Now, take the quotient 16 and divide it again by 2.

$$16 \div 2 = 8$$

So, 16 can be written as $16 = 2 imes 8$

1. Repeat until the quotient is 1

Keep dividing the quotient by the smallest prime number until you reach 1.

$$8 \div 2 = 4$$ $$4 \div 2 = 2$$ $$2 \div 2 = 1$$

So, each of these quotients can also be written as $8 = 2 imes 4$, $4 = 2 imes 2$, and $2 = 2 imes 1$

1. Write down all the prime factors

Combining all these, the prime factorization of 32 is

$$32 = 2 imes 2 imes 2 imes 2 imes 2 = 2^5$$

The final answer is $2^5$