800,199

3⁵ × 37 × 89

800,199 factors as 3^5 × 37 × 89. Its 24 positive divisors give a proper-divisor sum of 444,681, so this integer is deficient. The Collatz stopping time is 193 steps.

Prime Factor Structure

Factorization String 3^5 × 37 × 89

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,244,880

Proper Divisor Sum 444,681

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #800171 ← → #800209

Radix Representation

Decimal	800199
Binary	11000011010111000111 (20 bits)
Octal	0o3032707
Hexadecimal	0xC35C7

Divisor Catalog (24)

1 3 9 27 37 81 89 111 243 267 333 801 999 2,403 2,997 3,293 7,209 8,991 9,879 21,627 29,637 88,911 266,733 800,199

Collatz Trajectory (193 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

800,199 2,400,598 1,200,299 3,600,898 1,800,449 5,401,348 2,700,674 1,350,337 4,051,012 2,025,506 1,012,753 3,038,260 1,519,130 759,565 2,278,696 1,139,348 569,674 284,837 854,512 427,256 213,628 106,814 53,407 160,222 80,111 240,334 120,167 360,502 180,251 540,754 270,377 811,132 405,566 202,783 608,350 304,175 912,526 456,263 1,368,790 684,395 2,053,186 1,026,593 3,079,780 1,539,890 769,945 2,309,836 1,154,918 577,459 1,732,378 866,189 2,598,568 1,299,284 649,642 324,821 974,464 487,232 243,616 121,808 60,904 30,452

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