809,550

2 × 3² × 5² × 7 × 257

809,550 factors as 2 × 3^2 × 5^2 × 7 × 257. Its 72 positive divisors give a proper-divisor sum of 1,685,826, so this integer is abundant. The Collatz stopping time is 100 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 5^2 × 7 × 257

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,495,376

Proper Divisor Sum 1,685,826

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #809527 ← → #809563

Radix Representation

Decimal	809550
Binary	11000101101001001110 (20 bits)
Octal	0o3055116
Hexadecimal	0xC5A4E

Divisor Catalog (60 of 72)

1 2 3 5 6 7 9 10 14 15 18 21 25 30 35 42 45 50 63 70 75 90 105 126 150 175 210 225 257 315 350 450 514 525 630 771 1,050 1,285 1,542 1,575 1,799 2,313 2,570 3,150 3,598 3,855 4,626 5,397 6,425 7,710 8,995 10,794 11,565 12,850 16,191 17,990 19,275 23,130 26,985 32,382

Collatz Trajectory (100 steps to reach 1)

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

809,550 404,775 1,214,326 607,163 1,821,490 910,745 2,732,236 1,366,118 683,059 2,049,178 1,024,589 3,073,768 1,536,884 768,442 384,221 1,152,664 576,332 288,166 144,083 432,250 216,125 648,376 324,188 162,094 81,047 243,142 121,571 364,714 182,357 547,072 273,536 136,768 68,384 34,192 17,096 8,548 4,274 2,137 6,412 3,206 1,603 4,810 2,405 7,216 3,608 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382 191 574 287 862

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