Questions: Find the prime factorization of the composite number. 222

Find the prime factorization of the composite number. 222
Transcript text: Find the prime factorization of the composite number. \[ 222 \]
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Solution

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Solution Steps

To find the prime factorization of a composite number, we need to divide the number by the smallest prime number (starting from 2) and continue dividing the quotient by the smallest prime number until the quotient is 1. The prime factors are the prime numbers used in the division.

Step 1: Identify the Composite Number

The given composite number is \( 222 \).

Step 2: Perform Prime Factorization

To find the prime factorization of \( 222 \), we start dividing by the smallest prime number:

  1. \( 222 \div 2 = 111 \) (since \( 222 \) is even, we divide by \( 2 \)).
  2. Next, we check \( 111 \) for divisibility by the next smallest prime, \( 3 \):
    • \( 111 \div 3 = 37 \) (the sum of the digits \( 1 + 1 + 1 = 3 \) is divisible by \( 3 \)).
  3. Finally, \( 37 \) is a prime number and cannot be divided further.

Thus, the prime factorization of \( 222 \) is: \[ 222 = 2 \times 3 \times 37 \]

Final Answer

The prime factorization of \( 222 \) is \\(\boxed{2 \times 3 \times 37}\\).

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