8,092,800

2⁷ × 3² × 5² × 281

8,092,800 factors as 2^7 × 3^2 × 5^2 × 281. Its 144 positive divisors give a proper-divisor sum of 20,886,930, so this integer is abundant. The Collatz stopping time is 85 steps.

Prime Factor Structure

Factorization String 2^7 × 3^2 × 5^2 × 281

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 28,979,730

Proper Divisor Sum 20,886,930

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8092759 ← → #8092801

Radix Representation

Decimal	8092800
Binary	11110110111110010000000 (23 bits)
Octal	0o36676200
Hexadecimal	0x7B7C80

Divisor Catalog (60 of 144)

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 96 100 120 128 144 150 160 180 192 200 225 240 281 288 300 320 360 384 400 450 480 562 576 600 640 720 800 843 900 960 1,124

Collatz Trajectory (85 steps to reach 1)

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

8,092,800 4,046,400 2,023,200 1,011,600 505,800 252,900 126,450 63,225 189,676 94,838 47,419 142,258 71,129 213,388 106,694 53,347 160,042 80,021 240,064 120,032 60,016 30,008 15,004 7,502 3,751 11,254 5,627 16,882 8,441 25,324 12,662 6,331 18,994 9,497 28,492 14,246 7,123 21,370 10,685 32,056 16,028 8,014 4,007 12,022 6,011 18,034 9,017 27,052 13,526 6,763 20,290 10,145 30,436 15,218 7,609 22,828 11,414 5,707 17,122 8,561

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