Find the smallest 5-digit number which is exactly divisible by 36.

A number divisible by 36 must be divisible by both 4 and 9. Divisible by 4 ⇒ last two digits divisible by 4. Divisible by 9 ⇒ sum of digits divisible by 9. Smallest 5-digit number = 10000. Next number divisible by 4 = 10000 (already divisible by 4). Now check divisibility by 9: Sum of digits of 10000 = 1 → remainder 1 when divided by 9. To make it divisible by 9, add (9 − 1) = 8. New number = 10008 → check divisibility by 4 → 08 divisible by 4 ✅ 10008 ÷ 36 = 278 → remainder 0 ✅ Hence smallest 5-digit number divisible by 36 = 10008.