555

Here are quick facts and a tiny practice set for 555 you can use in exams:

Facts

• Prime factorization: 555 = 3 × 5 × 37
• Divisibility: divisible by 3, 5, and 15. Quotients: 555/3 = 185, 555/5 = 111, 555/15 = 37
• Roman numeral: DLV
• Binary: 1000101011₂
• Base 3: 202120₃
• Base 4: 20223₄
• Base 7: 1422₇
• Decimal property: 555 is a palindrome (555)

Quick problems (with answers)

1. Factor 555 and list all divisors.
   • 555 = 3 × 5 × 37. Divisors: 1, 3, 5, 15, 37, 111, 185, 555.
2. Convert 555 to base 4.
   • 555 = 2·4^4 + 0·4^3 + 2·4^2 + 2·4^1 + 3·4^0 → 20223₄.
3. Check if 555 = n(n+1)/2 for some integer n.
   • Solve n^2 + n − 1110 = 0. Discriminant Δ = 1 + 4440 = 4441, which is not a perfect square, so no integer n.
4. Convert 555 to base 2 and base 7 (quick check).
   • Base 2: 1000101011₂
   • Base 7: 1422₇

Would you like a tailored mini-problem set for a specific course (number theory, algebra, discrete math) or a particular difficulty level?