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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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How many positive 3-digit numbers are divisible by 12?
A 3-digit number ranges from 100 to 999. A number divisible by 12 must...
Find the smallest and largest 3-digit numbers divisible by 12:
Smallest: Check divisibility:
÷ 12 ≈ 8.33 → next integer is 9 → \(12 \times 9 = 108\)
Largest: 999 ÷ 12 ≈ 83.25 → largest integer is 83 → \(12 \times 83 = 9...
These form an arithmetic sequence: \(108, 120, \dots, 996\) with \(a =...
l = a + (n-1)d \implies 996 = 108 + (n-1) \cdot 12
= (n-1) \cdot 12 \implies n-1 = 74 \implies n = 75
There are \(\boxed{75}\) positive 3-digit numbers divisible by 12.**Qu...

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