What are the prime factors of 32?
Understand the Problem
The question is asking for the prime factors of the number 32. We will determine which prime numbers multiply together to give the product of 32.
Answer
The prime factorization of 32 is $2^5$.
Answer for screen readers
The prime factors of 32 are $2^5$.
Steps to Solve
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Identify the number to factor We are factoring the number 32.
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Start dividing by the smallest prime The smallest prime number is 2. We divide 32 by 2:
$$ 32 \div 2 = 16 $$
- Continue dividing by the same prime We continue dividing by 2 since it divides evenly:
$$ 16 \div 2 = 8 $$
- Keep dividing by the same prime We keep dividing by 2:
$$ 8 \div 2 = 4 $$
- One more division by the same prime Continue with 2:
$$ 4 \div 2 = 2 $$
- Final division by the same prime Finish by dividing 2 by 2:
$$ 2 \div 2 = 1 $$
- List the prime factors Since we repeatedly divided by 2, we find the prime factorization is:
$$ 32 = 2 \times 2 \times 2 \times 2 \times 2 $$
This can also be expressed as:
$$ 32 = 2^5 $$
The prime factors of 32 are $2^5$.
More Information
The number 32 is a power of 2, which is significant in various areas of mathematics and computer science, especially in binary systems.
Tips
- One common mistake is attempting to use prime numbers larger than 2 too early, as 32 is even and should first be divided by 2.
- Another mistake is not recognizing that multiple factors can be the same; for example, $2$ is used multiple times in this factorization.
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