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2. What is the prime factorization of 216 ?

Ask by Pollard Chambers. in the United States
Mar 11,2025

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The prime factorization of 216 is \(2^3 \times 3^3\).

Solución

**Step 1:** Begin by dividing \(216\) by the smallest prime number, \(2\): \[ 216 \div 2 = 108 \] **Step 2:** Continue dividing by \(2\): \[ 108 \div 2 = 54 \] **Step 3:** Divide by \(2\) once more: \[ 54 \div 2 = 27 \] At this point, we have: \[ 216 = 2^3 \times 27 \] **Step 4:** Factor \(27\) by recognizing it as a power of \(3\): \[ 27 = 3 \times 9 = 3 \times 3 \times 3 = 3^3 \] **Final Answer:** Thus, the prime factorization of \(216\) is: \[ 216 = 2^3 \times 3^3 \]

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Bonus Knowledge

To find the prime factorization of 216, start by dividing it by the smallest prime number, which is 2. You will find that 216 ÷ 2 = 108, then divide 108 by 2 to get 54, and again divide 54 by 2 to get 27. At this point, you switch to the next prime number, which is 3. Dividing 27 by 3 gives you 9, and dividing 9 by 3 gives you 3, and dividing 3 by 3 gets you down to 1. Therefore, the prime factorization of 216 is 2^3 × 3^3. Fun fact: 216 is a perfect cube! It equals 6 x 6 x 6 (or 6³), which means it aligns perfectly with geometry and even has practical uses in construction and design where cubic measurements matter. Just imagine building a perfect cube-shaped structure; 216 cubic units would give you an idea of the volume you need!

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