9,856,800

2⁵ × 3² × 5² × 37²

9,856,800 factors as 2^5 × 3^2 × 5^2 × 37^2. Its 162 positive divisors give a proper-divisor sum of 25,865,523, so this integer is abundant. The Collatz stopping time is 194 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5^2 × 37^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 162

Divisor Sum (σ) 35,722,323

Proper Divisor Sum 25,865,523

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #9856789 ← → #9856817

Radix Representation

Decimal	9856800
Binary	100101100110011100100000 (24 bits)
Octal	0o45463440
Hexadecimal	0x966720

Divisor Catalog (60 of 162)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 37 40 45 48 50 60 72 74 75 80 90 96 100 111 120 144 148 150 160 180 185 200 222 225 240 288 296 300 333 360 370 400 444 450 480 555 592 600 666 720 740

Collatz Trajectory (194 steps to reach 1)

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

9,856,800 4,928,400 2,464,200 1,232,100 616,050 308,025 924,076 462,038 231,019 693,058 346,529 1,039,588 519,794 259,897 779,692 389,846 194,923 584,770 292,385 877,156 438,578 219,289 657,868 328,934 164,467 493,402 246,701 740,104 370,052 185,026 92,513 277,540 138,770 69,385 208,156 104,078 52,039 156,118 78,059 234,178 117,089 351,268 175,634 87,817 263,452 131,726 65,863 197,590 98,795 296,386 148,193 444,580 222,290 111,145 333,436 166,718 83,359 250,078 125,039 375,118

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