Write the prime factorization of 27.
Understand the Problem
The question is asking for the prime factorization of the number 27, which involves breaking down the number into its prime components.
Answer
The prime factorization of 27 is $3^3$.
Answer for screen readers
The prime factorization of 27 is $3^3$.
Steps to Solve
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Identify if 27 is a prime number First, determine if 27 is a prime number. A prime number has only two distinct positive divisors: 1 and itself. Since 27 has divisors other than 1 and 27, it is not a prime number.
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Start dividing by the smallest prime number We begin by dividing 27 by the smallest prime number, which is 2. Since 27 is odd, it can't be divided by 2.
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Move to the next smallest prime number (3) Now try dividing 27 by 3: $$ 27 \div 3 = 9 $$ So, we can say that $27 = 3 \times 9$.
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Continue breaking down the quotient (9) Next, we can continue factoring 9 by dividing by 3 again: $$ 9 \div 3 = 3 $$ Thus, we can express 9 as $9 = 3 \times 3$.
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Combine all factors Now, we can combine all the factors we have obtained: $$ 27 = 3 \times 9 = 3 \times (3 \times 3) = 3^3 $$
The prime factorization of 27 is $3^3$.
More Information
The prime factorization shows that 27 is made up entirely of the prime number 3, multiplied by itself three times. This means 27 can be represented as ( 3^3 ), which equals 27.
Tips
- Assuming divisibility by 2: A common mistake is trying to divide 27 by 2 before determining that it's not even. Always check if the number is even before dividing by 2.
- Skipping steps in factorization: Some may try to jump to the answer without showing each stage of division, which can lead to incorrect conclusions.
