Study Guide · Chapter 18
2.16 Divisibility by 17
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Rule (Osculator, subtractive): Multiply last digit by 5, subtract from remaining number. Repeat. Example: Check 1,003. Last digit 3, ×5=15. Remaining=100. 100-15=85. 85 ÷ 17=5 → divisible by 17.
Example 2: Check whether 1,122 is divisible by 17. Last digit 2, ×5=10. Remaining=112. 112-10=102. Again: last digit 2, ×5=10. Remaining=10. 10-10=0 → divisible by 17 (direct check: 1122=17×66 ✓).
Example 3: Check whether 2,006 is divisible by 17. Last digit 6, ×5=30. Remaining=200. 200-30=170. Since 170=17×10, divisible by 17 → 2,006 is divisible by 17 (2006=17×118 ✓).
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