Questions: What is the prime factorization of 195 ? Use the × button or type the * key on your keyboard. For exponents, use the a^b button or the ^ key on your keyboard. If a number is prime, enter the number itself.

Solution Steps

First, we check if 195 is divisible by the smallest prime number, which is 2. Since 195 is odd, it is not divisible by 2.

Next, we check for divisibility by 3. The sum of the digits of 195 is \(1 + 9 + 5 = 15\), which is divisible by 3. Therefore, 195 is divisible by 3.

Divide 195 by 3:

\[ 195 \div 3 = 65 \]

So, we have:

\[ 195 = 3 \times 65 \]

Next, we factor 65. Check for divisibility by the smallest prime numbers:

• 65 is not divisible by 2 (since it is odd).
• The sum of the digits of 65 is \(6 + 5 = 11\), which is not divisible by 3.
• 65 ends in 5, so it is divisible by 5.

Divide 65 by 5:

\[ 65 \div 5 = 13 \]

So, we have:

\[ 65 = 5 \times 13 \]

The number 13 is a prime number.

Final Answer