Question 10 of 31intermediate🔧 ApplyNumerical2 marks

Find the smallest multiple of 9 with no odd digits.

Correct Answer

Given: Find the smallest multiple of 9 with no odd digits.

Rule: A number is divisible by 9 if the sum of its digits is divisible by 9. Even digits are: 0, 2, 4, 6, 8

Checking 1-digit multiples: 9 — has odd digit

Checking 2-digit multiples: 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 — all have odd digits

Checking 3-digit multiples: 108 — has 1 (odd) 117 — has 1, 7 (odd) ... 288 — digits are 2, 8, 8 (all even) Sum = 2 + 8 + 8 = 18 18 ÷ 9 = 2 ✓

Answer: 288

Exercise: Figure it Out (Section 2) | Q: 2 | (Page Page 15)
For More Understanding

Explanation

The chapter discusses divisibility by 9. We need a multiple of 9 using only even digits (0, 2, 4, 6, 8). Checking multiples of 9: 9 (has 9), 18 (has 1), 27 (has 7), 36 (has 3), 45 (has 5), 54 (has 5), 63 (has 3), 72 (has 7), 81 (has 1), 90 (has 9), 99 (has 9), 108 (has 1), continuing... 288 has digits 2, 8, 8 (all even) and 2+8+8=18 which is divisible by 9.

Solution Steps

  1. Identify that we need a multiple of 9 using only even digits (0, 2, 4, 6, 8)

  2. Check 1-digit and 2-digit multiples of 9 — all contain odd digits

  3. Check 3-digit multiples starting from 108

  4. 288 has digits 2, 8, 8 (all even)

  5. Verify: 2 + 8 + 8 = 18, which is divisible by 9

  6. 288 is the smallest multiple of 9 with no odd digits

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