13,282,920

2³ × 3³ × 5 × 7² × 251

13,282,920 factors as 2^3 × 3^3 × 5 × 7^2 × 251. Its 192 positive divisors give a proper-divisor sum of 38,427,480, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^3 × 3^3 × 5 × 7^2 × 251

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 192

Divisor Sum (σ) 51,710,400

Proper Divisor Sum 38,427,480

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #13282909 ← → #13282921

Radix Representation

Decimal	13282920
Binary	110010101010111001101000 (24 bits)
Octal	0o62527150
Hexadecimal	0xCAAE68

Divisor Catalog (60 of 192)

1 2 3 4 5 6 7 8 9 10 12 14 15 18 20 21 24 27 28 30 35 36 40 42 45 49 54 56 60 63 70 72 84 90 98 105 108 120 126 135 140 147 168 180 189 196 210 216 245 251 252 270 280 294 315 360 378 392 420 441

Collatz Trajectory (135 steps to reach 1)

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

13,282,920 6,641,460 3,320,730 1,660,365 4,981,096 2,490,548 1,245,274 622,637 1,867,912 933,956 466,978 233,489 700,468 350,234 175,117 525,352 262,676 131,338 65,669 197,008 98,504 49,252 24,626 12,313 36,940 18,470 9,235 27,706 13,853 41,560 20,780 10,390 5,195 15,586 7,793 23,380 11,690 5,845 17,536 8,768 4,384 2,192 1,096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395

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