2⁵ × 3² × 5 × 53

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 53

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 265,356

Proper Divisor Sum 189,036

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #76303 ← → #76333

Radix Representation

Decimal	76320
Binary	10010101000100000 (17 bits)
Octal	0o225040
Hexadecimal	0x12A20

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 53 60 72 80 90 96 106 120 144 159 160 180 212 240 265 288 318 360 424 477 480 530 636 720 795 848 954 1,060 1,272 1,440 1,590 1,696 1,908 2,120 2,385 2,544 3,180 3,816 4,240

Collatz Trajectory (107 steps to reach 1)

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

76,320 38,160 19,080 9,540 4,770 2,385 7,156 3,578 1,789 5,368 2,684 1,342 671 2,014 1,007 3,022 1,511 4,534 2,267 6,802 3,401 10,204 5,102 2,551 7,654 3,827 11,482 5,741 17,224 8,612 4,306 2,153 6,460 3,230 1,615 4,846 2,423 7,270 3,635 10,906 5,453 16,360 8,180 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494

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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