2⁷ × 3² × 5 × 7

Prime Factor Structure

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

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 159,120

Proper Divisor Sum 118,800

Digit Sum / Digital Root 9 (Root: 9)

Adjacent Primes #40289 ← → #40343

Radix Representation

Decimal	40320
Binary	1001110110000000 (16 bits)
Octal	0o116600
Hexadecimal	0x9D80

Divisor Catalog (60 of 96)

1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 28 30 32 35 36 40 42 45 48 56 60 63 64 70 72 80 84 90 96 105 112 120 126 128 140 144 160 168 180 192 210 224 240 252 280 288 315 320 336 360 384 420

Collatz Trajectory (44 steps to reach 1)

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

40,320 20,160 10,080 5,040 2,520 1,260 630 315 946 473 1,420 710 355 1,066 533 1,600 800 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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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