808,200

2³ × 3² × 5² × 449

808,200 factors as 2^3 × 3^2 × 5^2 × 449. Its 72 positive divisors give a proper-divisor sum of 1,912,050, so this integer is abundant. The Collatz stopping time is 206 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 5^2 × 449

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,720,250

Proper Divisor Sum 1,912,050

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #808187 ← → #808211

Radix Representation

Decimal	808200
Binary	11000101010100001000 (20 bits)
Octal	0o3052410
Hexadecimal	0xC5508

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 18 20 24 25 30 36 40 45 50 60 72 75 90 100 120 150 180 200 225 300 360 449 450 600 898 900 1,347 1,796 1,800 2,245 2,694 3,592 4,041 4,490 5,388 6,735 8,082 8,980 10,776 11,225 13,470 16,164 17,960 20,205 22,450 26,940 32,328 33,675 40,410

Collatz Trajectory (206 steps to reach 1)

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

808,200 404,100 202,050 101,025 303,076 151,538 75,769 227,308 113,654 56,827 170,482 85,241 255,724 127,862 63,931 191,794 95,897 287,692 143,846 71,923 215,770 107,885 323,656 161,828 80,914 40,457 121,372 60,686 30,343 91,030 45,515 136,546 68,273 204,820 102,410 51,205 153,616 76,808 38,404 19,202 9,601 28,804 14,402 7,201 21,604 10,802 5,401 16,204 8,102 4,051 12,154 6,077 18,232 9,116 4,558 2,279 6,838 3,419 10,258 5,129

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