Identifying the Prime Factor in a Three-Digit Number ?12

Question

I am a three-digit number ?12 ?12

Which prime factor will surely appear among my first factors?

Video Solution

Step-by-Step Solution

To solve this problem, we will make use of divisibility rules, particularly focusing on the rule for 2.

  • Step 1: Analyze the given number form, ?12 ?12 , which indicates the number is a three-digit integer ending with the digits 12.
  • Step 2: Apply divisibility rules. Note the last digit of 12 12 is an even number, which is 2. By the rule of divisibility by 2, any number ending in an even number is divisible by 2.
  • Step 3: Since the last digit is 2, it confirms the number is divisible by 2. Therefore, 2 is a prime factor of the number ?12 ?12 .

Given the options, 2 2 is the only prime factor that will certainly appear among the first factors of any number ending with 12, as other numbers such as 3, 7, or 11 do not have guaranteed divisibility given non-fixed sum of digits or specific rules not directly applicable.

Therefore, the solution to the problem is 2 2 .

Answer

2 2