555

Do you mean the number 555 (math) or something like the 555 timer circuit? If you’re studying math, here are quick facts and a couple of practice bits about 555:

Quick facts

• Prime factorization: 555 = 3 × 5 × 37
• It is square-free; number of divisors d(555) = (1+1)(1+1)(1+1) = 8
• Sum of all divisors σ(555) = (1+3)(1+5)(1+37) = 4 × 6 × 38 = 912
• Sum of proper divisors = 912 − 555 = 357 (so 555 is deficient, since 357 < 555)
• Base representations: binary 1000101011₂; octal 1053₈; hexadecimal 0x22B
• Digit facts: sum of digits = 15, digital root = 6; divisible by 3 and 5

Practice problems

• Find the number of divisors of 555. Answer: 8.
• Verify whether 555 is divisible by 9 or 11. (Digits sum 15 → not divisible by 9; test for 11 gives false.)
• Compute the sum of all divisors of 555 (done above as 912) and the sum of its proper divisors (357).

Would you like more problems (different difficulty), or a quick explanation of any of these concepts? If you meant the 555 timer, tell me and I’ll switch topics.