2³ × 3⁴ × 43

Prime Factor Structure

Factorization String 2^3 × 3^4 × 43

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 79,860

Proper Divisor Sum 51,996

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #27851 ← → #27883

Radix Representation

Decimal	27864
Binary	110110011011000 (15 bits)
Octal	0o66330
Hexadecimal	0x6CD8

Divisor Catalog (40)

1 2 3 4 6 8 9 12 18 24 27 36 43 54 72 81 86 108 129 162 172 216 258 324 344 387 516 648 774 1,032 1,161 1,548 2,322 3,096 3,483 4,644 6,966 9,288 13,932 27,864

Collatz Trajectory (90 steps to reach 1)

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

27,864 13,932 6,966 3,483 10,450 5,225 15,676 7,838 3,919 11,758 5,879 17,638 8,819 26,458 13,229 39,688 19,844 9,922 4,961 14,884 7,442 3,721 11,164 5,582 2,791 8,374 4,187 12,562 6,281 18,844 9,422 4,711 14,134 7,067 21,202 10,601 31,804 15,902 7,951 23,854 11,927 35,782 17,891 53,674 26,837 80,512 40,256 20,128 10,064 5,032 2,516 1,258 629 1,888 944 472 236 118 59 178

Active Feeder Network

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

Feeder #1,448,561 Feeder #6,970,568 Feeder #2,947,453 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174

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