Find the prime factorization of 48.
Understand the Problem
The question is asking for the prime factorization of the number 48, which means we need to break down 48 into its prime factors.
Answer
The prime factorization of 48 is $2^4 \times 3^1$.
Answer for screen readers
The prime factorization of 48 is $2^4 \times 3^1$.
Steps to Solve
- Divide by the smallest prime number
Start by dividing 48 by the smallest prime number, which is 2.
$$ 48 \div 2 = 24 $$
- Continue dividing by 2
Since 24 is also even, we can divide it again by 2.
$$ 24 \div 2 = 12 $$
- Keep dividing by 2
Next, divide 12 by 2 again.
$$ 12 \div 2 = 6 $$
- Divide by 2 one more time
Now, divide 6 by 2.
$$ 6 \div 2 = 3 $$
- Identify the last factor
Finally, 3 is a prime number, so we stop here.
The prime factorization of 48 is then the product of the prime numbers we used to divide it.
The prime factorization of 48 is $2^4 \times 3^1$.
More Information
The prime factorization is useful in various areas of mathematics, such as simplifying fractions, finding least common multiples, and making calculations easier. The number 48 can be expressed as the product of its prime factors four times the number 2 and once the number 3.
Tips
- Forgetting to stop at the prime number: Ensure you recognize when you've arrived at a prime number like 3.
- Not keeping track of the number of times you divide by the same prime: It's essential to count how many times each prime factor is used so that you can express the prime factorization correctly.
