Which of these are divisible by 18? - Decision Point

Understanding the Context

Understanding Divisibility by 18

Divisibility by 18 depends on two key mathematical rules:

• The number must be divisible by 2 (back-to-back evenness: last digit is even).
  
• The number must also be divisible by 9 (sum of digits is divisible by 9).

Because 18 = 2 × 9 (and 2 and 9 are coprime), a number is divisible by 18 if and only if it meets both criteria.

Key Insights

Examples of Numbers Divisible by 18

Before answering your specific question (“which of these”), here are classic examples:

• 18 → ✅ Divisible: ends in 8 (even), digit sum = 1 + 8 = 9 (divisible by 9)
  
• 36 → ✅ Divisible: ends in 6 (even), digit sum = 3 + 6 = 9 (divisible by 9)
  
• 54 → ✅ Divisible: ends in 4, digit sum = 5 + 4 = 9
  
• 90 → ✅ Divisible: even, digit sum = 9 + 0 = 9
  
• 126 → ✅ Divisible: ends in 6, digit sum = 1 + 2 + 6 = 9

How to Check Divisibility by 18 in Practice

1. Check if the last digit is even — if not, skip (not divisible by 2).
   
2. Add all digits — if the total is divisible by 9, then the number is divisible by 18.
   
3. Avoid division errors by verifying with actual division if unsure.

Final Thoughts

Numbers Not Divisible by 18

Common examples include:

• 10 → Ends in 0 (even), but digit sum = 1, not divisible by 9
  
• 17 → Odd and digit sum = 8, not divisible by 2 or 9
  
• 45 → Digit sum = 9, but ends in 5 (odd), not divisible by 2
  
• 29 → Not even and digit sum = 11, not divisible by either

Applying This to Your List: Which Are Divisible by 18?

Although you haven’t listed specific numbers, here’s how to evaluate your set:

• Start by filtering even numbers.
  
• Then sum the digits of those. If the result is divisible by 9, then that number is divisible by 18.