What is the prime factorization of 576?
Understand the Problem
The question is asking for the prime factorization of the number 576, which involves breaking it down into its prime factors.
Answer
$2^5 \times 3^2$
Answer for screen readers
The prime factorization of 576 is $2^5 \times 3^2$.
Steps to Solve
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Find the smallest prime factor
Start with the smallest prime number, which is 2. Check if 576 is divisible by 2. Since $576 \div 2 = 288$, we find that 2 is indeed a prime factor. -
Continue dividing by the smallest prime factor
Now, we can divide 288 by 2 again:
$288 \div 2 = 144$.
We repeat this process:
- $144 \div 2 = 72$
- $72 \div 2 = 36$
- $36 \div 2 = 18$
- $18 \div 2 = 9$
At this point, 9 is no longer divisible by 2.
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Switch to the next smallest prime (3)
Now, we check the next prime number, which is 3. Since $9 \div 3 = 3$, we can divide again:
$3 \div 3 = 1$. -
List all prime factors
We have divided 576 completely. Count the factors of each prime:
- From the factor of 2: We divided by 2 a total of 5 times.
- From the factor of 3: We divided by 3 a total of 2 times.
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Write the prime factorization
Thus, the prime factorization of 576 can be expressed as:
$$ 576 = 2^5 \times 3^2 $$
The prime factorization of 576 is $2^5 \times 3^2$.
More Information
The number 576 is a composite number, and its prime factorization reveals that it can be expressed as a product of prime factors, which helps in various mathematical applications like finding the greatest common divisor (GCD) or simplifying fractions.
Tips
A common mistake is to overlook the need to try all prime factors and only to focus on small primes at the beginning. It's important to try different prime factors systematically until reaching 1.
