853,380

2² × 3² × 5 × 11 × 431

853,380 factors as 2^2 × 3^2 × 5 × 11 × 431. Its 72 positive divisors give a proper-divisor sum of 1,977,084, so this integer is abundant. The Collatz stopping time is 74 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 11 × 431

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,830,464

Proper Divisor Sum 1,977,084

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #853357 ← → #853387

Radix Representation

Decimal	853380
Binary	11010000010110000100 (20 bits)
Octal	0o3202604
Hexadecimal	0xD0584

Divisor Catalog (60 of 72)

1 2 3 4 5 6 9 10 11 12 15 18 20 22 30 33 36 44 45 55 60 66 90 99 110 132 165 180 198 220 330 396 431 495 660 862 990 1,293 1,724 1,980 2,155 2,586 3,879 4,310 4,741 5,172 6,465 7,758 8,620 9,482 12,930 14,223 15,516 18,964 19,395 23,705 25,860 28,446 38,790 42,669

Collatz Trajectory (74 steps to reach 1)

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

853,380 426,690 213,345 640,036 320,018 160,009 480,028 240,014 120,007 360,022 180,011 540,034 270,017 810,052 405,026 202,513 607,540 303,770 151,885 455,656 227,828 113,914 56,957 170,872 85,436 42,718 21,359 64,078 32,039 96,118 48,059 144,178 72,089 216,268 108,134 54,067 162,202 81,101 243,304 121,652 60,826 30,413 91,240 45,620 22,810 11,405 34,216 17,108 8,554 4,277 12,832 6,416 3,208 1,604 802 401 1,204 602 301 904

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