Find the sum of the smallest and largest prime factors of $10101$.
To find the prime factors of $10101$, I could try dividing it by different prime numbers, starting from the smallest ones, until I get a quotient of $1$. Alternatively, I could use a divisibility rule or a calculator to speed up the process. For example, I notice that $10101$ ends in $1$, which means it is not divisible by $2$, $5$, or $10$. I also notice that the sum of its digits is $3$, which means it is divisible by $3$. So, I can divide $10101$ by $3$ and get $3367$. Now, I need to check if $3367$ is prime or not. I can use a calculator to test some primes, such as $7$, $11$, $13$, etc. I find that $3367$ is divisible by $13$, and get $259$. Next, I need to check if $259$ is prime or not. I can use a calculator to test some primes, such as $17$, $19$, $23$, etc. I find that $259$ is divisible by $37$, and get $7$. Finally, I have reached a prime quotient, so I can stop dividing. The prime factors of $10101$ are $3$, $13$, $37$, and $7$. The smallest one is $3$ and the largest one is $37$. To find their sum, I just need to add them: $3 + 37 = 40$. 