λ
Ratio Atlas
Atlas › Integer Profiles › Node 32,400
32,400
24 × 34 × 52
Abundant Even Composite Square (√ = 180)

Prime Factor Structure

Factorization String 2^4 × 3^4 × 5^2
Distinct Prime Factors 3
Square Status Yes (√32400 = 180)
Abundance Measure Abundant

Analytical Properties

Total Divisors 75
Divisor Sum (σ) 116,281
Proper Divisor Sum 83,881
Digit Sum / Digital Root 9 (Root: 9)
Adjacent Primes #32381 ← → #32401

Radix Representation

Decimal 32400
Binary 111111010010000 (15 bits)
Octal 0o77220
Hexadecimal 0x7E90

Divisor Catalog (60 of 75)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 36 40 45 48 50 54 60 72 75 80 81 90 100 108 120 135 144 150 162 180 200 216 225 240 270 300 324 360 400 405 432 450 540 600 648 675 720 810 900 1,080 1,200 1,296

Collatz Trajectory (160 steps to reach 1)

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

32,400 16,200 8,100 4,050 2,025 6,076 3,038 1,519 4,558 2,279 6,838 3,419 10,258 5,129 15,388 7,694 3,847 11,542 5,771 17,314 8,657 25,972 12,986 6,493 19,480 9,740 4,870 2,435 7,306 3,653 10,960 5,480 2,740 1,370 685 2,056 1,028 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214

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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