What is the prime factorization of 324?
Understand the Problem
The question is asking for the prime factorization of the number 324, which involves breaking it down into its prime factors.
Answer
The prime factorization of 324 is $2^2 \times 3^4$.
Answer for screen readers
The prime factorization of 324 is $2^2 \times 3^4$.
Steps to Solve
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Start with the number Begin with the number 324 that we want to factor into primes.
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Divide by the smallest prime The smallest prime number is 2. Check if 324 is divisible by 2. Calculate: $$ 324 \div 2 = 162 $$ So, $ 324 = 2 \times 162 $.
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Continue factoring Now, take 162 and divide it by 2 again since it is still even: $$ 162 \div 2 = 81 $$ Thus, $ 162 = 2 \times 81 $, giving us: $$ 324 = 2^2 \times 81 $$.
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Move to the next prime Next, try to factor 81. The smallest prime factor of 81 is 3. Divide 81 by 3: $$ 81 \div 3 = 27 $$ So, $ 81 = 3 \times 27 $.
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Continue dividing by 3 Now, factor 27: $$ 27 \div 3 = 9 $$ Thus, $ 27 = 3 \times 9 $, leading to: $$ 81 = 3^2 \times 9 $$.
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Factor 9 Factor 9 by dividing by 3: $$ 9 \div 3 = 3 $$ So, $ 9 = 3 \times 3 = 3^2 $.
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Combine all factors Now, putting all the prime factors together: $$ 324 = 2^2 \times 3^4 $$.
The prime factorization of 324 is $2^2 \times 3^4$.
More Information
Prime factorization is useful for simplifying fractions and solving problems in number theory. The number 324 can also be seen as a perfect square since it equals $18^2$.
Tips
- Forgetting to divide by the smallest prime first, which can lead to more complex calculations.
- Stopping the factorization prematurely; ensure you factor until all remaining factors are prime.
