prime factorization of 648
Understand the Problem
The question is asking for the prime factorization of the number 648, which means we need to express 648 as a product of its prime factors.
Answer
The prime factorization of 648 is $2^3 \times 3^4$.
Answer for screen readers
The prime factorization of 648 is $2^3 \times 3^4$.
Steps to Solve
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Start with the number Begin with the number 648 that we need to factor.
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Divide by the smallest prime number Divide 648 by the smallest prime number, which is 2. $$ 648 \div 2 = 324 $$
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Continue dividing by 2 Since 324 is even, divide it by 2 again. $$ 324 \div 2 = 162 $$
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Divide by 2 once more Continue with 162. $$ 162 \div 2 = 81 $$
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Switch to the next prime number Now, 81 is no longer even, so we switch to the next smallest prime, which is 3. $$ 81 \div 3 = 27 $$
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Keep dividing by 3 Continue with 27. $$ 27 \div 3 = 9 $$
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Divide by 3 again Next, divide 9. $$ 9 \div 3 = 3 $$
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Final division by 3 Finally, divide 3. $$ 3 \div 3 = 1 $$
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Collect all the prime factors Now, we collect all prime factors from the divisions: 2, 2, 2, 3, 3, 3.
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Write the prime factorization Express 648 as a product of its prime factors: $$ 648 = 2^3 \times 3^4 $$
The prime factorization of 648 is $2^3 \times 3^4$.
More Information
The prime factorization process breaks down any number into its basic building blocks, which are prime numbers. Recognizing the prime factors can be useful in various mathematical applications, including finding the least common multiple and greatest common divisor.
Tips
- Misidentifying prime numbers: Always double-check which numbers are prime. Remember that 1 is not a prime number.
- Forgetting to divide completely: Ensure each division is carried out correctly until reaching 1.
