Which of the following numbers is not divisible by 14?

To determine if a number is divisible by 14, it must be divisible by both of its prime factors, 2 and 7.

Step-by-Step Analysis

A number is divisible by 2 if it is even (ends in 0, 2, 4, 6, or 8). A number is divisible by 7 if the result of subtracting twice the last digit from the remaining leading truncated number is divisible by 7.

Let's test each option:

• Option A: 3542

  • Ends in 2 (Even, divisible by 2).

  • Check 7: 354 - (2 * 2) = 350. Since 350 is divisible by 7 (350 / 7 = 50), 3542 is divisible by 14.

• Option B: 2086

  • Ends in 6 (Even, divisible by 2).

  • Check 7: 208 - (6 * 2) = 208 - 12 = 196. Since 196 is divisible by 7 (196 / 7 = 28), 2086 is divisible by 14.

• Option C: 1998

  • Ends in 8 (Even, divisible by 2).

  • Check 7: 199 - (8 * 2) = 199 - 16 = 183. Since 183 is not divisible by 7 (183 / 7 ≈ 26.14), 1998 is not divisible by 14.

• Option D: 2996

  • Ends in 6 (Even, divisible by 2).

  • Check 7: 299 - (6 * 2) = 299 - 12 = 287. Since 287 is divisible by 7 (287 / 7 = 41), 2996 is divisible by 14.