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Problem #73 · October 8, 2026

Divisibility rules

If the four-digit number 47a2‾\overline{47a2} is divisible by 33, find the greatest value of the digit aa.
  1. A2
  2. B3
  3. C5
  4. D8
  5. E9

WORKED EXAMPLE

Solution

By the divisibility rule for 33, the sum of the digits, the number 4+7+a+2=13+a4+7+a+2 = 13+a, must be divisible by 33. Suitable values: 13+a=15;18;2113+a = 15; 18; 21, that is, a∈{2;5;8}a \in \{2; 5; 8\}. The greatest of them is a=8a = 8.
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