200,832

2⁷ × 3 × 523

Starting at 200,832, the Collatz iteration reaches 1 after 41 steps. The first transition is 100416; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^7 × 3 × 523

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 534,480

Proper Divisor Sum 333,648

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #200807 ← → #200843

Radix Representation

Decimal	200832
Binary	110001000010000000 (18 bits)
Octal	0o610200
Hexadecimal	0x31080

Divisor Catalog (32)

1 2 3 4 6 8 12 16 24 32 48 64 96 128 192 384 523 1,046 1,569 2,092 3,138 4,184 6,276 8,368 12,552 16,736 25,104 33,472 50,208 66,944 100,416 200,832

Collatz Trajectory (41 steps to reach 1)

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

200,832 100,416 50,208 25,104 12,552 6,276 3,138 1,569 4,708 2,354 1,177 3,532 1,766 883 2,650 1,325 3,976 1,988 994 497 1,492 746 373 1,120 560 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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