Pinpointing Prime Factors: Which Always Appears in a Two-Digit Number?

To solve this problem, follow these steps:

• Step 1: Recognize that a two-digit number ending in 0 can be expressed as $10 \times n$, where $n$ is an integer from 1 to 9.
• Step 2: Since the number ends in 0, it is essentially divisible by 10.
• Step 3: The prime factorization of 10 is $10 = 2 \times 5$.
• Step 4: Among these prime factors, we are asked which one surely appears. That is, any number ending in 0 will certainly include 5 as a prime factor.
• Step 5: Therefore, the prime factor that will surely appear is $5$.

Therefore, the solution to the problem is that the prime factor is $5$.