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.
Answer
$2^5$
Answer for screen readers
The final answer is $2^5$
Steps to Solve
- 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 $32 = 2 imes 16$
- 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 $16 = 2 imes 8$
- 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 $2 = 2 imes 1$
- 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 $2^5$
More Information
Prime factorization is the process of expressing a composite number as a product of its prime factors. For example, the prime factorization of 32 shows that it is composed entirely of the prime number 2.
Tips
A common mistake is stopping the division too early. Make sure to continue dividing until the final quotient is 1.
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