449,580

2² × 3 × 5 × 59 × 127

449,580 factors as 2^2 × 3 × 5 × 59 × 127. Its 48 positive divisors give a proper-divisor sum of 840,660, so this integer is abundant. The Collatz stopping time is 112 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 59 × 127

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,290,240

Proper Divisor Sum 840,660

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #449569 ← → #449591

Radix Representation

Decimal	449580
Binary	1101101110000101100 (19 bits)
Octal	0o1556054
Hexadecimal	0x6DC2C

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 30 59 60 118 127 177 236 254 295 354 381 508 590 635 708 762 885 1,180 1,270 1,524 1,770 1,905 2,540 3,540 3,810 7,493 7,620 14,986 22,479 29,972 37,465 44,958 74,930 89,916 112,395 149,860 224,790 449,580

Collatz Trajectory (112 steps to reach 1)

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

449,580 224,790 112,395 337,186 168,593 505,780 252,890 126,445 379,336 189,668 94,834 47,417 142,252 71,126 35,563 106,690 53,345 160,036 80,018 40,009 120,028 60,014 30,007 90,022 45,011 135,034 67,517 202,552 101,276 50,638 25,319 75,958 37,979 113,938 56,969 170,908 85,454 42,727 128,182 64,091 192,274 96,137 288,412 144,206 72,103 216,310 108,155 324,466 162,233 486,700 243,350 121,675 365,026 182,513 547,540 273,770 136,885 410,656 205,328 102,664

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