555

Not sure what you want with “555.” Do you want quick math practice around the number 555, or something else? Here are a few quick 555-related prep notes and problems you can use right away.

Quick facts about 555

• Prime factorization: 555 = 3 × 5 × 37
• Divisors: 1, 3, 5, 15, 37, 111, 185, 555 (8 divisors)
• Sum of divisors: 912
• 555 in bases:
  • Binary: 1000101011
  • Hexadecimal: 0x22B (since 2×256 + 2×16 + 11 = 555)
• Divisibility: divisible by 3, 5, and 15 (555 = 15 × 37)

Practice problems

1. Verify the prime factorization and list all divisors. Answer: 3 × 5 × 37; divisors as above.
2. Compute the sum of all divisors. Answer: 912.
3. Convert 555 to binary and to hex. Answer: binary 1000101011, hex 0x22B.
4. What is 555 modulo 7? (Hint: 7 × 79 = 553, so remainder is 2.)
5. If you write 555 as a product of two numbers closest to sqrt(555), what pair do you get? (sqrt(555) ≈ 23.6; closest pair with the factors 3, 5, 37 would be 15 × 37 = 555.)

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