How many three-digit numbers are divisible by 6?

Given data

• Three-digit range: 100 to 999 (inclusive).
• Divisible by 6 ⇔ divisible by 2 and 3.

Concept / Approach

• Count multiples of 6 between 100 and 999 using arithmetic progression count or floor-division method.

Step-by-step calculation

Smallest 3-digit multiple: 102 = 6×17Largest 3-digit multiple: 996 = 6×166Count = ((996 − 102)/6) + 1 = (894/6) + 1 = 149 + 1 = 150

Alternative check

⌊999/6⌋ − ⌊99/6⌋ = 166 − 16 = 150 ✔

Common pitfalls

• Forgetting the +1 in the term-count formula or mistakenly including 100/999.

Final Answer

150