198,450

2 × 3⁴ × 5² × 7²

198,450 factors as 2 × 3^4 × 5^2 × 7^2. Its 90 positive divisors give a proper-divisor sum of 442,971, so this integer is abundant. The Collatz stopping time is 142 steps.

Prime Factor Structure

Factorization String 2 × 3^4 × 5^2 × 7^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 90

Divisor Sum (σ) 641,421

Proper Divisor Sum 442,971

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #198439 ← → #198461

Radix Representation

Decimal	198450
Binary	110000011100110010 (18 bits)
Octal	0o603462
Hexadecimal	0x30732

Divisor Catalog (60 of 90)

1 2 3 5 6 7 9 10 14 15 18 21 25 27 30 35 42 45 49 50 54 63 70 75 81 90 98 105 126 135 147 150 162 175 189 210 225 245 270 294 315 350 378 405 441 450 490 525 567 630 675 735 810 882 945 1,050 1,134 1,225 1,323 1,350

Collatz Trajectory (142 steps to reach 1)

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

198,450 99,225 297,676 148,838 74,419 223,258 111,629 334,888 167,444 83,722 41,861 125,584 62,792 31,396 15,698 7,849 23,548 11,774 5,887 17,662 8,831 26,494 13,247 39,742 19,871 59,614 29,807 89,422 44,711 134,134 67,067 201,202 100,601 301,804 150,902 75,451 226,354 113,177 339,532 169,766 84,883 254,650 127,325 381,976 190,988 95,494 47,747 143,242 71,621 214,864 107,432 53,716 26,858 13,429 40,288 20,144 10,072 5,036 2,518 1,259

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