768,096

2⁵ × 3³ × 7 × 127

Prime Factor Structure

Factorization String 2^5 × 3^3 × 7 × 127

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 2,580,480

Proper Divisor Sum 1,812,384

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #768073 ← → #768101

Radix Representation

Decimal	768096
Binary	10111011100001100000 (20 bits)
Octal	0o2734140
Hexadecimal	0xBB860

Divisor Catalog (60 of 96)

1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 72 84 96 108 112 126 127 144 168 189 216 224 252 254 288 336 378 381 432 504 508 672 756 762 864 889 1,008 1,016 1,143 1,512 1,524 1,778 2,016 2,032 2,286 2,667 3,024

Collatz Trajectory (149 steps to reach 1)

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

768,096 384,048 192,024 96,012 48,006 24,003 72,010 36,005 108,016 54,008 27,004 13,502 6,751 20,254 10,127 30,382 15,191 45,574 22,787 68,362 34,181 102,544 51,272 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

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