72,000

2⁶ × 3² × 5³

Prime Factor Structure

Factorization String 2^6 × 3^2 × 5^3

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 84

Divisor Sum (σ) 257,556

Proper Divisor Sum 185,556

Digit Sum / Digital Root 9 (Root: 9)

Adjacent Primes #71999 ← → #72019

Radix Representation

Decimal	72000
Binary	10001100101000000 (17 bits)
Octal	0o214500
Hexadecimal	0x11940

Divisor Catalog (60 of 84)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 45 48 50 60 64 72 75 80 90 96 100 120 125 144 150 160 180 192 200 225 240 250 288 300 320 360 375 400 450 480 500 576 600 720 750 800 900 960 1,000 1,125

Collatz Trajectory (50 steps to reach 1)

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

72,000 36,000 18,000 9,000 4,500 2,250 1,125 3,376 1,688 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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