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Ratio Atlas
Atlas › Integer Profiles › Node 27,000
27,000
23 × 33 × 53
Abundant Even Composite

Prime Factor Structure

Factorization String 2^3 × 3^3 × 5^3
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 93,600
Proper Divisor Sum 66,600
Digit Sum / Digital Root 9 (Root: 9)
Adjacent Primes #26993 ← → #27011

Radix Representation

Decimal 27000
Binary 110100101111000 (15 bits)
Octal 0o64570
Hexadecimal 0x6978

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 9 10 12 15 18 20 24 25 27 30 36 40 45 50 54 60 72 75 90 100 108 120 125 135 150 180 200 216 225 250 270 300 360 375 450 500 540 600 675 750 900 1,000 1,080 1,125 1,350 1,500 1,800 2,250 2,700 3,000 3,375 4,500 5,400

Collatz Trajectory (139 steps to reach 1)

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

27,000 13,500 6,750 3,375 10,126 5,063 15,190 7,595 22,786 11,393 34,180 17,090 8,545 25,636 12,818 6,409 19,228 9,614 4,807 14,422 7,211 21,634 10,817 32,452 16,226 8,113 24,340 12,170 6,085 18,256 9,128 4,564 2,282 1,141 3,424 1,712 856 428 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175

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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