555

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Quick facts about 555

• Factorization: 555 = 3 × 5 × 37
• Divisors: 1, 3, 5, 15, 37, 111, 185, 555 (8 divisors)
• Roman numeral: 555 = DLV
• Base representations:
  • Binary: 555 = 1000101011_2
  • Hexadecimal: 0x22B
  • Base-3: 555 = 202120_3
• Digit properties: sum of digits = 15; product of digits = 125; digital root = 6

Practice question (with solution)

• Question: Solve 3x + 5y = 555 for integers x, y.
• Method: Work modulo 3. Since 555 ≡ 0 (mod 3) and 5y ≡ 2y (mod 3), we need 2y ≡ 0 (mod 3) ⇒ y ≡ 0 (mod 3). Let y = 3t. Then 3x + 5(3t) = 555 ⇒ 3x + 15t = 555 ⇒ x + 5t = 185 ⇒ x = 185 − 5t.
• General integer solution: (x, y) = (185 − 5t, 3t) for any integer t.
• If you want nonnegative solutions, require 185 − 5t ≥ 0 and 3t ≥ 0 ⇒ t ∈ {0, 1, 2, ..., 37}.

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