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

I am a two-digit number $?0$

Which prime factor will surely appear among my first factors?

Video Solution

Solution Steps

00:00 Which factor definitely appears in the primary factors of the number?

00:04 The ones digit is 0

00:06 Let's try dividing 10 by each of the factors and see what's possible

00:20 Let's try dividing various tens by factor 5 and see what divides

00:25 In fact, any number with tens digit and ones digit being 0 is divisible by 5

00:30 And this is the solution to the question

Step-by-Step Solution

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 $5$ .