Which Prime Factor Lurks in the Two-Digit Number ?4

Question

I am a two-digit number ?4 ?4

Which prime factor will surely appear among my first factors?

Video Solution

Step-by-Step Solution

To solve this problem, let's analyze the numbers:

  • Step 1: Identify that all numbers of the form ?4 ?4 end with the digit 4, which is even.
  • Step 2: Apply the divisibility rule for 2: A number ending in an even digit is divisible by 2.
  • Step 3: Recognize that since all such numbers are even due to ending in 4, each number is divisible by 2.

Therefore, every number ending in 4 has 2 as a factor.

To further clarify, consider some examples: 14, 24, 34, ..., 94. These can all be divided by 2.

Therefore, the prime factor that will surely appear among the factors of any number in the form "?4""?4" is 2 2 .

Answer

2 2