19,992,000

2⁶ × 3 × 5³ × 7² × 17

19,992,000 factors as 2^6 × 3 × 5^3 × 7^2 × 17. Its 336 positive divisors give a proper-divisor sum of 61,316,448, so this integer is abundant. The Collatz stopping time is 164 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 5^3 × 7^2 × 17

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 336

Divisor Sum (σ) 81,308,448

Proper Divisor Sum 61,316,448

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #19991989 ← → #19992001

Radix Representation

Decimal	19992000
Binary	1001100010000110111000000 (25 bits)
Octal	0o114206700
Hexadecimal	0x1310DC0

Divisor Catalog (60 of 336)

1 2 3 4 5 6 7 8 10 12 14 15 16 17 20 21 24 25 28 30 32 34 35 40 42 48 49 50 51 56 60 64 68 70 75 80 84 85 96 98 100 102 105 112 119 120 125 136 140 147 150 160 168 170 175 192 196 200 204 210

Collatz Trajectory (164 steps to reach 1)

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

19,992,000 9,996,000 4,998,000 2,499,000 1,249,500 624,750 312,375 937,126 468,563 1,405,690 702,845 2,108,536 1,054,268 527,134 263,567 790,702 395,351 1,186,054 593,027 1,779,082 889,541 2,668,624 1,334,312 667,156 333,578 166,789 500,368 250,184 125,092 62,546 31,273 93,820 46,910 23,455 70,366 35,183 105,550 52,775 158,326 79,163 237,490 118,745 356,236 178,118 89,059 267,178 133,589 400,768 200,384 100,192 50,096 25,048 12,524 6,262 3,131 9,394 4,697 14,092 7,046 3,523

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