What is the prime factor of 512?
Understand the Problem
The question is asking for the prime factorization of the number 512. To find this, we will break down 512 into its prime components.
Answer
$2^9$
Answer for screen readers
The prime factorization of 512 is $2^9$.
Steps to Solve
- Divide by the Smallest Prime Start by dividing 512 by the smallest prime number, which is 2.
$$ 512 \div 2 = 256 $$
- Continue Dividing by 2 Keep dividing the result by 2, since it's even.
$$ 256 \div 2 = 128 $$
- Repeat the Process Continue dividing by 2.
$$ 128 \div 2 = 64 $$
- Keep Dividing Continue with the same process.
$$ 64 \div 2 = 32 $$
- Continue Dividing Keep dividing by 2 again.
$$ 32 \div 2 = 16 $$
- Repeat Division Divide by 2 once more.
$$ 16 \div 2 = 8 $$
- Final Divisions Keep dividing by 2.
$$ 8 \div 2 = 4 $$
- Last Division Finally, divide one last time by 2.
$$ 4 \div 2 = 2 $$
- Final Prime Now that you have 2, divide it once more.
$$ 2 \div 2 = 1 $$
At this point, you cannot divide any further as you've reached 1.
- Collecting Factors Count the number of times you divided by 2. The number 512 can be expressed as a product of its prime factors:
$$ 512 = 2^9 $$
The prime factorization of 512 is $2^9$.
More Information
The number 512 is a power of 2, which is notable in many mathematical applications, including computer science where binary systems are based on powers of 2.
Tips
- Forgetting to check for larger prime factors: Always start with the smallest and continue with the smallest until you can’t divide anymore.
- Miscounting the number of times 2 is a factor: It's essential to keep careful track of how many times you divide by 2.
Thank you for voting!
