What is the prime factorization of 48?
Understand the Problem
The question is asking for the prime factorization of the number 48, which involves breaking down the number 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
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Start with the number We begin with the number 48, and we want to break it down into prime factors.
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Divide by the smallest prime number The smallest prime number is 2. We divide 48 by 2:
$$ 48 \div 2 = 24 $$
So, 2 is a prime factor. -
Repeat with the quotient Now we take the quotient 24 and divide it again by 2:
$$ 24 \div 2 = 12 $$
So we have another factor of 2. -
Continue dividing by 2 Next, we continue with 12:
$$ 12 \div 2 = 6 $$
Another factor of 2. -
Continue again with 6 Next, we divide 6 by 2:
$$ 6 \div 2 = 3 $$
We've found yet another factor of 2. -
Factor the last quotient Now we have the number 3, which is also prime. So we stop here.
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Compile the prime factors All the prime factors we found are 2 (four times) and 3 (one time). We can express the prime factorization of 48 as:
$$ 48 = 2^4 \times 3^1 $$
The prime factorization of 48 is ( 2^4 \times 3^1 ).
More Information
The prime factorization shows how 48 can be expressed as a product of prime numbers. Understanding prime factorization is useful in various areas of math, including simplifying fractions, finding least common multiples, and solving problems in number theory.
Tips
- Forgetting to include all factors: Make sure to continue dividing until you can only factor out prime numbers.
- Stopping the factorization too early: Always ensure to check if the quotient can still be divided by a prime number.
