The number $1254216$ is divisible by which of the following numbers?

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Accepted Answer

**Solution:**

1. **Divisibility by 8:**
   - A number is divisible by 8 if its last three digits form a number divisible by 8.
   - Last three digits of $1254216$ are $216$.
   - $216 \div 8 = 27$, which is an integer.
   - Hence, $1254216$ is divisible by $8$.

2. **Divisibility by 11:**
   - Sum of digits in odd positions (from right to left): $1 + 5 + 2 + 1 = 9$
   - Sum of digits in even positions: $2 + 4 + 6 = 12$
   - Difference $= |9 - 12| = 3$, which is not a multiple of $11$.
   - Hence, $1254216$ is not divisible by $11$.

3. **Divisibility by 5:**
   - A number is divisible by 5 if its last digit is $0$ or $5$.
   - Last digit of $1254216$ is $6$.
   - Hence, it is not divisible by $5$.

4. **Divisibility by 16:**
   - A number is divisible by 16 if its last four digits form a number divisible by 16.
   - Last four digits are $4216$.
   - $4216 \div 16 = 263.5$, not an integer.
   - Hence, $1254216$ is not divisible by $16$.

**Answer:** The number $1254216$ is divisible only by $8$.

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