First, find the smallest 3-digit number divisible by 11:
["How to Find the Smallest 3-Digit Number Divisible by 11: A Step-by-Step Guide", "When learning about divisibility, one common question is: What is the smallest 3-digit number divisible by 11? This is a foundational problem in number theory that helps build understanding of divisibility rules and basic arithmetic. In this article, we’ll walk you through the logical steps to find the answer efficiently, while also explaining the key concept of divisibility by 11.", "---", "### Understanding the Problem", "A three-digit number ranges from 100 to 999. The task is to identify the smallest number in this range that can be evenly divided by 11 — meaning, when divided by 11, the result is a whole number with no remainder.", "---", "### Why Learn the Smallest 3-Digit Multiple of 11?", "Finding the smallest 3-digit number divisible by 11 builds your understanding of:", "- Divisibility rules\n- Number patterns\n- Basic division and rounding concepts", "It’s also a practical starting point for exploring larger divisibility questions.", "---", "### Step 1: Divide the Lower Bound by 11", "To find the smallest 3-digit multiple of 11, begin by dividing the smallest 3-digit number, 100, by 11:", "[\n100 \div 11 \approx 9.09\n]", "Since 9.09 is not a whole number, 100 is not divisible by 11.", "---", "### Step 2: Round Up to the Next Whole Number", "The next whole number after 9.09 is 10. This means:", "[\n11 \ imes 10 = 110\n]", "Check if 110 is a 3-digit number — yes, it is.", "---", "### Step 3: Confirm Divisibility", "Verify that 110 divided by 11 gives a whole number:", "[\n110 \div 11 = 10\n]", "✅ Since the result is a whole number, 110 is divisible by 11.", "---", "### Step 4: Verify It’s the Smallest 3-Digit Multiple", "We checked that 100 ÷ 11 ≈ 9.09 (not divisible), and the next multiple occurred at 11 × 10 = 110 — a valid 3-digit number.", "Therefore, 110 is indeed the smallest 3-digit number divisible by 11.", "---", "### Summary", "- The smallest 3-digit number is 100\n- 100 ÷ 11 ≈ 9.09 → not divisible\n- 11 × 10 = 110 → divisible by 11 and a 3-digit number\n- ✅ Answer: 110", "---", "### Practical Tip for Future Problems", "For any divisor:", "1. Start with the smallest 3-digit number (100).\n2. Divide by the divisor and round up to the nearest whole number.\n3. Multiply that whole number by the divisor to get the smallest 3-digit multiple.", "This method simplifies finding smallest/largest multiples across all number ranges.", "---", "### Further Reading", "- Explore divisibility rules for 3, 7, and 13\n- Learn how to find the largest 3-digit multiple of any number\n- Practice with divisibility by 9, 12, and 7", "---", "Understanding small multiples like the smallest 3-digit number divisible by 11 strengthens numerical intuition and prepares learners for more advanced math topics. Use this step-by-step guide next time you’re faced with a similar problem — and remember: Start small, divide, and confirm!", "---", "Keywords: smallest 3-digit number divisible by 11, find smallest multiple of 11, divisibility rules, 3-digit number divisibility, mathematical foundation, number theory basics, how to divide 100 by 11, math tips for students", "Meta Description: Discover how to find the smallest 3-digit number divisible by 11 through step-by-step division and verification — perfect for learners and math beginners. Learn key divisibility rules and arithmetic shortcuts."]
