1,002,840

2³ × 3 × 5 × 61 × 137

Starting at 1,002,840, the Collatz iteration reaches 1 after 113 steps. The first transition is 501420; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 61 × 137

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 3,080,160

Proper Divisor Sum 2,077,320

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #1002821 ← → #1002851

Radix Representation

Decimal	1002840
Binary	11110100110101011000 (20 bits)
Octal	0o3646530
Hexadecimal	0xF4D58

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 61 120 122 137 183 244 274 305 366 411 488 548 610 685 732 822 915 1,096 1,220 1,370 1,464 1,644 1,830 2,055 2,440 2,740 3,288 3,660 4,110 5,480 7,320 8,220 8,357 16,440 16,714 25,071 33,428 41,785 50,142 66,856 83,570 100,284 125,355 167,140 200,568

Collatz Trajectory (113 steps to reach 1)

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

1,002,840 501,420 250,710 125,355 376,066 188,033 564,100 282,050 141,025 423,076 211,538 105,769 317,308 158,654 79,327 237,982 118,991 356,974 178,487 535,462 267,731 803,194 401,597 1,204,792 602,396 301,198 150,599 451,798 225,899 677,698 338,849 1,016,548 508,274 254,137 762,412 381,206 190,603 571,810 285,905 857,716 428,858 214,429 643,288 321,644 160,822 80,411 241,234 120,617 361,852 180,926 90,463 271,390 135,695 407,086 203,543 610,630 305,315 915,946 457,973 1,373,920

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