855,000

2³ × 3² × 5⁴ × 19

855,000 factors as 2^3 × 3^2 × 5^4 × 19. Its 120 positive divisors give a proper-divisor sum of 2,190,900, so this integer is abundant. The Collatz stopping time is 219 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 5^4 × 19

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 3,045,900

Proper Divisor Sum 2,190,900

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #854999 ← → #855031

Radix Representation

Decimal	855000
Binary	11010000101111011000 (20 bits)
Octal	0o3205730
Hexadecimal	0xD0BD8

Divisor Catalog (60 of 120)

1 2 3 4 5 6 8 9 10 12 15 18 19 20 24 25 30 36 38 40 45 50 57 60 72 75 76 90 95 100 114 120 125 150 152 171 180 190 200 225 228 250 285 300 342 360 375 380 450 456 475 500 570 600 625 684 750 760 855 900

Collatz Trajectory (219 steps to reach 1)

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

855,000 427,500 213,750 106,875 320,626 160,313 480,940 240,470 120,235 360,706 180,353 541,060 270,530 135,265 405,796 202,898 101,449 304,348 152,174 76,087 228,262 114,131 342,394 171,197 513,592 256,796 128,398 64,199 192,598 96,299 288,898 144,449 433,348 216,674 108,337 325,012 162,506 81,253 243,760 121,880 60,940 30,470 15,235 45,706 22,853 68,560 34,280 17,140 8,570 4,285 12,856 6,428 3,214 1,607 4,822 2,411 7,234 3,617 10,852 5,426

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