First, find the smallest 3-digit number divisible by 7.
["# How to Find the Smallest 3-Digit Number Divisible by 7 – A Simple Math Guide", "Finding the smallest three-digit number divisible by 7 is a straightforward math task that helps sharpen your number sense and understanding of divisibility. Whether you’re studying basic arithmetic, preparing for a math test, or just curious about numbers, this guide will walk you through the process step by step.", "## Understanding What It Means to Be Divisible by 7", "A number is divisible by 7 if, when divided by 7, the remainder is zero. In mathematical terms, a number ( n ) is divisible by 7 if there exists an integer ( k ) such that:", "[\nn = 7 \ imes k\n]", "Our goal is to find the smallest three-digit number (i.e., starting from 100) that satisfies this condition.", "## Step-by-Step: Finding the Smallest 3-Digit Number Divisible by 7", "### Step 1: Identify the smallest 3-digit number\nThe smallest 3-digit number is 100.", "### Step 2: Divide 100 by 7 to check divisibility\nPerform the division:\n[\n100 \div 7 \approx 14.2857\n]\nThis quotient is not an integer — it’s a non-integer, so 100 is not divisible by 7.", "### Step 3: Increment and check successive multiples\nSince 100 ÷ 7 ≈ 14.2857, the next whole number is 15. We now multiply:\n[\n7 \ imes 15 = 105\n]", "### Step 4: Confirm 105 is a 3-digit number and divisible by 7\n105 is clearly between 100 and 999 — it’s a 3-digit number.\nCheck divisibility:\n[\n105 \div 7 = 15 \quad \ ext{(exactly, no remainder)}\n]", "✅ Success!", "## Why 105 Is the Answer", "Because:\n- 105 is the first multiple of 7 after 100,\n- It’s the smallest three-digit number satisfying the divisibility rule,\n- It confirms the pattern of multiples of 7 increments starting from 14 (14×7=98, two-digit) up to 15 (105, three-digit).", "## Summary", "The smallest three-digit number divisible by 7 is:\n105", "## Practice Tip", "If you want to find the next few such numbers, simply continue adding 7 to 105:\n105, 112, 119, 126, ...", "This works because any number + 7 is the next multiple of 7.", "---", "Key Takeaways:\n- Find the smallest 3-digit number (100), then divide by 7.\n- The next whole number quotient multiplied by 7 gives the smallest 3-digit multiple.\n- Check via division or repeated addition to confirm.", "Mastering such basic divisibility problems builds a strong foundation for more advanced math!"]
