555

Nice. What would you like to do with the number 555? Here are a few quick options. Pick one, or tell me your topic and I’ll tailor problems.

Quick facts about 555:

• Prime factorization: 3 × 5 × 37
• Divisible by: 3 and 5
• Roman numeral: DLV
• Hex: 0x22B
• Binary: 1000101011
• 555 seconds = 9 minutes 15 seconds
• Number of divisors: 8
• Sum of divisors: 912

Practice problems (with answers):

1. Factorize 555 completely: 3 × 5 × 37
2. Solve x^2 + 2x − 555 = 0
   • Discriminant: Δ = 4 + 2220 = 2224 = 16 × 139
   • x = (-2 ± √2224)/2 = -1 ± √139 ≈ -12.79 or 10.79
3. What is 7^555 mod 9?
   • 7 ≡ -2 (mod 9); (-2)^555 ≡ -(2^555) (mod 9)
   • 2^6 ≡ 1 (mod 9); 555 ≡ 3 (mod 6) → 2^555 ≡ 2^3 ≡ 8
   • So result ≡ -8 ≡ 1 (mod 9)
   • Remainder: 1
4. If a rectangle has sides x and x+2 with area 555, find x (real numbers)
   • x(x+2) = 555 → x^2 + 2x − 555 = 0
   • x = -1 ± √139 ≈ -12.79 or 10.79

Want more problems on a specific topic (algebra, number theory, calculus, etc.) or a quick quiz on a different angle of 555?