478,233

3² × 7 × 7591

478,233 factors as 3^2 × 7 × 7591. Its 12 positive divisors give a proper-divisor sum of 311,335, so this integer is deficient. The Collatz stopping time is 200 steps.

Prime Factor Structure

Factorization String 3^2 × 7 × 7591

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 789,568

Proper Divisor Sum 311,335

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #478213 ← → #478241

Radix Representation

Decimal	478233
Binary	1110100110000011001 (19 bits)
Octal	0o1646031
Hexadecimal	0x74C19

Divisor Catalog (12)

1 3 7 9 21 63 7,591 22,773 53,137 68,319 159,411 478,233

Collatz Trajectory (200 steps to reach 1)

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

478,233 1,434,700 717,350 358,675 1,076,026 538,013 1,614,040 807,020 403,510 201,755 605,266 302,633 907,900 453,950 226,975 680,926 340,463 1,021,390 510,695 1,532,086 766,043 2,298,130 1,149,065 3,447,196 1,723,598 861,799 2,585,398 1,292,699 3,878,098 1,939,049 5,817,148 2,908,574 1,454,287 4,362,862 2,181,431 6,544,294 3,272,147 9,816,442 4,908,221 14,724,664 7,362,332 3,681,166 1,840,583 5,521,750 2,760,875 8,282,626 4,141,313 12,423,940 6,211,970 3,105,985 9,317,956 4,658,978 2,329,489 6,988,468 3,494,234 1,747,117 5,241,352 2,620,676 1,310,338 655,169

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