What are the prime factors of the number 216?

• (1) 2 × 2 × 3 × 3 × 3
• (2) 2 × 2 × 2 × 3 × 3 × 3
• (3) 2 × 2 × 2 × 3 × 3 × 3 × 3
• (4) None of these

The prime factors of the number 216 can be determined by breaking it down into its simplest components. To find the prime factorization, we can repeatedly divide by the smallest prime numbers.

Step-by-Step Factorization

Starting with 216:

• 216 is even, so we divide by 2: 216 ÷ 2 = 108
• 108 is also even: 108 ÷ 2 = 54
• 54 is still even: 54 ÷ 2 = 27
• 27 is not even, so we divide by the next prime number, which is 3: 27 ÷ 3 = 9
• 9 can also be divided by 3: 9 ÷ 3 = 3
• Finally, 3 is a prime number: 3 ÷ 3 = 1

Final Prime Factorization

The complete prime factorization of 216 is:

• 2 × 2 × 2 × 3 × 3 × 3

This can also be expressed as:

• 2³ × 3³

Correct Answer

From the options provided, the correct choice is:

• (2) 2 × 2 × 2 × 3 × 3 × 3