Study Guide · Chapter 15
2.13 Divisibility by 14
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Rule: Divisible by both 2 and 7.
Example 1: Is 4,928 divisible by 14? Even? Last digit 8 → yes. Divisible by 7? Osculator: last digit 8, double=16, remaining=492, 492-16=476; last digit 6, double=12, remaining=47, 47-12=35, divisible by 7 → yes. Since both hold, 4,928 is divisible by 14 (4928÷14=352 exact ✓).
Example 2: Is 6,314 divisible by 14? Even? Last digit 4 → yes. Divisible by 7? Osculator: last digit 4, double=8, remaining=631, 631-8=623; from Section 2.6 Example 5 we already know 623=7×89 is divisible by 7. Since both hold, 6,314 is divisible by 14 (6314÷14=451 exact ✓).
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