2³ × 3 × 5 × 7² × 13

Prime Factor Structure

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

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 287,280

Proper Divisor Sum 210,840

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #76423 ← → #76441

Radix Representation

Decimal	76440
Binary	10010101010011000 (17 bits)
Octal	0o225230
Hexadecimal	0x12A98

Divisor Catalog (60 of 96)

1 2 3 4 5 6 7 8 10 12 13 14 15 20 21 24 26 28 30 35 39 40 42 49 52 56 60 65 70 78 84 91 98 104 105 120 130 140 147 156 168 182 195 196 210 245 260 273 280 294 312 364 390 392 420 455 490 520 546 588

Collatz Trajectory (107 steps to reach 1)

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

76,440 38,220 19,110 9,555 28,666 14,333 43,000 21,500 10,750 5,375 16,126 8,063 24,190 12,095 36,286 18,143 54,430 27,215 81,646 40,823 122,470 61,235 183,706 91,853 275,560 137,780 68,890 34,445 103,336 51,668 25,834 12,917 38,752 19,376 9,688 4,844 2,422 1,211 3,634 1,817 5,452 2,726 1,363 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494

Active Feeder Network

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

Feeder #6,573,969 Feeder #2,443,427 Feeder #6,845,105 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174

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