prime factorization of 512
Understand the Problem
The question is asking for the prime factorization of the number 512, which involves breaking it down into its prime components.
Answer
The prime factorization of 512 is $2^9$.
Answer for screen readers
The prime factorization of 512 is $2^9$.
Steps to Solve
- Start with the Number
Begin with the number you want to factor, which is 512.
- Divide by the Smallest Prime Number
The smallest prime number is 2. Check if 512 is divisible by 2. Since it's even, we can divide:
$$ 512 \div 2 = 256 $$
- Continue Dividing by 2
Now, take 256 and divide it by 2 again:
$$ 256 \div 2 = 128 $$
Repeat this step for 128:
$$ 128 \div 2 = 64 $$
And for 64:
$$ 64 \div 2 = 32 $$
Now for 32:
$$ 32 \div 2 = 16 $$
Next for 16:
$$ 16 \div 2 = 8 $$
Continue with 8:
$$ 8 \div 2 = 4 $$
And for 4:
$$ 4 \div 2 = 2 $$
Finally, divide 2 by 2:
$$ 2 \div 2 = 1 $$
- List the Prime Factorization
Now, count how many times you divided by 2.
You divided by 2 a total of 9 times.
Thus, the prime factorization of 512 is:
$$ 512 = 2^9 $$
The prime factorization of 512 is $2^9$.
More Information
The number 512 is a power of two, specifically $2^9$. Powers of two are common in computing, where they represent binary structures and memory capacities.
Tips
- Confusing the order of operations by trying to divide by odd prime numbers first. Always start with the smallest prime, which is 2.
