2 × 3² × 7 × 13 × 17

Prime Factor Structure

Factorization String 2 × 3^2 × 7 × 13 × 17

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 78,624

Proper Divisor Sum 50,778

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #27827 ← → #27847

Radix Representation

Decimal	27846
Binary	110110011000110 (15 bits)
Octal	0o66306
Hexadecimal	0x6CC6

Divisor Catalog (48)

1 2 3 6 7 9 13 14 17 18 21 26 34 39 42 51 63 78 91 102 117 119 126 153 182 221 234 238 273 306 357 442 546 663 714 819 1,071 1,326 1,547 1,638 1,989 2,142 3,094 3,978 4,641 9,282 13,923 27,846

Collatz Trajectory (59 steps to reach 1)

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

27,846 13,923 41,770 20,885 62,656 31,328 15,664 7,832 3,916 1,958 979 2,938 1,469 4,408 2,204 1,102 551 1,654 827 2,482 1,241 3,724 1,862 931 2,794 1,397 4,192 2,096 1,048 524 262 131 394 197 592 296 148 74 37 112 56 28 14 7 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 #6,449,649 Feeder #6,177,699 Feeder #4,494,486 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174

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