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Answer :
To find the prime factorization of 198, we need to break it down into its prime factors. Here's a step-by-step process to achieve that:
1. Start with the smallest prime number, 2, and check if it divides 198 evenly. Since 198 is an even number, it is divisible by 2.
- 198 divided by 2 equals 99.
- So, the first prime factor is 2.
2. Move to the next prime number, which is 3. Check if 99 is divisible by 3. To check for divisibility by 3, you can add the digits of 99 (9 + 9 = 18), and since 18 is divisible by 3, so is 99.
- 99 divided by 3 equals 33.
- So, 3 is a prime factor and 99 = 3 × 33.
3. Continue with the number 33, and check divisibility by 3 again. Following the same logic as before, 3 divides 33 evenly.
- 33 divided by 3 equals 11.
- So, another factor of 3 is found: 33 = 3 × 11.
4. Now, we have 11 left. Check if 11 is a prime number. It is because its only divisors are 1 and 11 itself.
Therefore, the complete prime factorization of 198 is:
198 = 2 × 3 × 3 × 11, or in exponential terms, 198 = 2^1 × 3^2 × 11^1.
This means the prime factors of 198 are 2, 3 (with an exponent of 2, representing two 3s), and 11.
1. Start with the smallest prime number, 2, and check if it divides 198 evenly. Since 198 is an even number, it is divisible by 2.
- 198 divided by 2 equals 99.
- So, the first prime factor is 2.
2. Move to the next prime number, which is 3. Check if 99 is divisible by 3. To check for divisibility by 3, you can add the digits of 99 (9 + 9 = 18), and since 18 is divisible by 3, so is 99.
- 99 divided by 3 equals 33.
- So, 3 is a prime factor and 99 = 3 × 33.
3. Continue with the number 33, and check divisibility by 3 again. Following the same logic as before, 3 divides 33 evenly.
- 33 divided by 3 equals 11.
- So, another factor of 3 is found: 33 = 3 × 11.
4. Now, we have 11 left. Check if 11 is a prime number. It is because its only divisors are 1 and 11 itself.
Therefore, the complete prime factorization of 198 is:
198 = 2 × 3 × 3 × 11, or in exponential terms, 198 = 2^1 × 3^2 × 11^1.
This means the prime factors of 198 are 2, 3 (with an exponent of 2, representing two 3s), and 11.
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