What is the least prime factor of $7^4 - 7^3$?
I want to find the smallest prime number that divides $7^4 - 7^3$ evenly. I notice that both terms in the subtraction have a factor of $7^3$, so I can factor it out: $7^4 - 7^3 = 7^3(7 - 1)$. This simplifies the expression to $7^3 \times 6$. Now I just need to find the smallest prime factor of $6$, since I already know that $7^3$ is not divisible by any prime smaller than $7$. The smallest prime factor of $6$ is $2$, so the answer is $2$. 