555

Do you mean the number 555 for math prep, or the Thai joke/emoji meaning “hahaha” with 5 = ha? If you’re prepping for exams, here are quick properties and a few practice prompts about 555:

Quick properties

• Decimal factorization: 555 = 3 × 5 × 37
• Divisibility: divisible by 3 and by 5; not by 9, 11, etc.
• Digits sum: 5+5+5 = 15
• Roman numeral: 555 = DLV
• Binary: 55510 = 1000101011₂

Useful computations

• Euler’s totient φ(555) = 288
• Number of positive divisors d(555) = 8
• Sum of divisors σ(555) = 912 (because 555 = 3 × 5 × 37 and σ(n) for squarefree n = (1+3)(1+5)(1+37) = 4×6×38 = 912)

Practice prompts you can try

• List all divisors of 555.
• Verify φ(555) by the product formula: φ(555) = 555 × (1−1/3) × (1−1/5) × (1−1/37) = 288.
• Compute the gcd of 555 and another number, e.g., gcd(555, 1000) and explain.
• If n = 555 and m = 37, what is gcd(n, m) and lcm(n, m)? (Hint: use prime factorization.)

If you intended something else (like a specific course topic or more problems), tell me the subject and I’ll tailor the questions and solutions.