2⁵ × 3³ × 7 × 13

Prime Factor Structure

Factorization String 2^5 × 3^3 × 7 × 13

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 282,240

Proper Divisor Sum 203,616

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #78623 ← → #78643

Radix Representation

Decimal	78624
Binary	10011001100100000 (17 bits)
Octal	0o231440
Hexadecimal	0x13320

Divisor Catalog (60 of 96)

1 2 3 4 6 7 8 9 12 13 14 16 18 21 24 26 27 28 32 36 39 42 48 52 54 56 63 72 78 84 91 96 104 108 112 117 126 144 156 168 182 189 208 216 224 234 252 273 288 312 336 351 364 378 416 432 468 504 546 624

Collatz Trajectory (138 steps to reach 1)

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

78,624 39,312 19,656 9,828 4,914 2,457 7,372 3,686 1,843 5,530 2,765 8,296 4,148 2,074 1,037 3,112 1,556 778 389 1,168 584 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526

Active Feeder Network

Other feeder batches with open delivery windows. Each feeder keeps its own target batch.

Feeder #7,737,779 Feeder #685,881 Feeder #2,871,188 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174

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