800,821

7 × 233 × 491

800,821 has digital root 1. The neighboring primes are 800801 and 800861; its proper-divisor sum differs from the starting integer by -680,618.

Prime Factor Structure

Factorization String 7 × 233 × 491

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 921,024

Proper Divisor Sum 120,203

Digit Sum / Digital Root 19 (Root: 1)

Adjacent Primes #800801 ← → #800861

Radix Representation

Decimal	800821
Binary	11000011100000110101 (20 bits)
Octal	0o3034065
Hexadecimal	0xC3835

Divisor Catalog (8)

1 7 233 491 1,631 3,437 114,403 800,821

Collatz Trajectory (92 steps to reach 1)

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

800,821 2,402,464 1,201,232 600,616 300,308 150,154 75,077 225,232 112,616 56,308 28,154 14,077 42,232 21,116 10,558 5,279 15,838 7,919 23,758 11,879 35,638 17,819 53,458 26,729 80,188 40,094 20,047 60,142 30,071 90,214 45,107 135,322 67,661 202,984 101,492 50,746 25,373 76,120 38,060 19,030 9,515 28,546 14,273 42,820 21,410 10,705 32,116 16,058 8,029 24,088 12,044 6,022 3,011 9,034 4,517 13,552 6,776 3,388 1,694 847

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