What is the prime factorization of 512?
Understand the Problem
The question is asking for the prime factorization of the number 512, which means breaking it down into the prime numbers that multiply together to give the original number.
Answer
The prime factorization of 512 is \( 2^9 \).
Answer for screen readers
The prime factorization of 512 is ( 2^9 ).
Steps to Solve
- Divide by the smallest prime number Start with the number 512 and divide it by the smallest prime number, which is 2.
$$ 512 \div 2 = 256 $$
- Continue dividing by 2 Keep dividing the result by 2 since it is still even and can be divided further.
$$ 256 \div 2 = 128 $$
- Repeat the division Continue the process of dividing by 2.
$$ 128 \div 2 = 64 $$
- Continue the division Keep dividing by 2.
$$ 64 \div 2 = 32 $$
- Repeat until odd Keep dividing by 2 until you can no longer divide evenly.
$$ 32 \div 2 = 16 $$ $$ 16 \div 2 = 8 $$ $$ 8 \div 2 = 4 $$ $$ 4 \div 2 = 2 $$ $$ 2 \div 2 = 1 $$
- Write the prime factorization Count the number of times you divided by 2. Since you divided by 2 a total of 9 times, we can express the prime factorization as:
$$ 512 = 2^9 $$
The prime factorization of 512 is ( 2^9 ).
More Information
The number 512 is a power of 2, specifically ( 2^9 ). This means that 512 can be expressed as multiplying 2 by itself 9 times. Powers of 2 are common in computing, especially in binary representations.
Tips
- Skipping Non-prime Factors: Make sure you only divide by prime numbers (like 2, 3, 5, etc.) during the factorization process.
- Miscounting Divisions: Carefully track how many times you divide by the prime until you reach 1.
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