555

Not sure what you want with “555.” Do you want math stuff involving the number 555, or were you aiming at a different subject? If you’re studying math, here are quick notes and a tiny problem set you can use right away.

Quick math facts about 555

• Factorization: 555 = 3 × 5 × 37
• Divisors: 1, 3, 5, 15, 37, 111, 185, 555 (eight divisors)
• Sum of divisors σ(555) = (1+3)(1+5)(1+37) = 4 × 6 × 38 = 912
• Sum of proper divisors = 912 − 555 = 357
• Digital root: 5+5+5 = 15 → 1+5 = 6
• 555 ends with 5, so divisible by 5; digits sum to 15, so divisible by 3; hence divisible by 15 (555 ÷ 15 = 37)
• 555 is a Harshad (Niven) number in base 10 (divisible by sum of digits)

Tiny practice set

1. List all positive divisors of 555 and verify there are 8.
2. Compute 555².
3. Compute 555 mod 37 and interpret the result.
4. Solve for x in 555x ≡ 1 (mod 7).
5. Is 555 a perfect number? (Answer: no; give a quick justification using proper divisors.)

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