8,003,380

2² × 5 × 7 × 11 × 5197

Starting at 8,003,380, the Collatz iteration reaches 1 after 93 steps. The first transition is 4001690; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 11 × 5197

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 20,958,336

Proper Divisor Sum 12,954,956

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #8003309 ← → #8003381

Radix Representation

Decimal	8003380
Binary	11110100001111100110100 (23 bits)
Octal	0o36417464
Hexadecimal	0x7A1F34

Divisor Catalog (48)

1 2 4 5 7 10 11 14 20 22 28 35 44 55 70 77 110 140 154 220 308 385 770 1,540 5,197 10,394 20,788 25,985 36,379 51,970 57,167 72,758 103,940 114,334 145,516 181,895 228,668 285,835 363,790 400,169 571,670 727,580 800,338 1,143,340 1,600,676 2,000,845 4,001,690 8,003,380

Collatz Trajectory (93 steps to reach 1)

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

8,003,380 4,001,690 2,000,845 6,002,536 3,001,268 1,500,634 750,317 2,250,952 1,125,476 562,738 281,369 844,108 422,054 211,027 633,082 316,541 949,624 474,812 237,406 118,703 356,110 178,055 534,166 267,083 801,250 400,625 1,201,876 600,938 300,469 901,408 450,704 225,352 112,676 56,338 28,169 84,508 42,254 21,127 63,382 31,691 95,074 47,537 142,612 71,306 35,653 106,960 53,480 26,740 13,370 6,685 20,056 10,028 5,014 2,507 7,522 3,761 11,284 5,642 2,821 8,464

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