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823,830

2 × 3 × 5 × 7 × 3923
Abundant Even Composite

823,830 factors as 2 × 3 × 5 × 7 × 3923. Its 32 positive divisors give a proper-divisor sum of 1,436,394, so this integer is abundant. The Collatz stopping time is 237 steps.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 7 × 3923
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 2,260,224
Proper Divisor Sum 1,436,394
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #823829 ← → #823831

Radix Representation

Decimal 823830
Binary 11001001001000010110 (20 bits)
Octal 0o3111026
Hexadecimal 0xC9216

Divisor Catalog (32)

1 2 3 5 6 7 10 14 15 21 30 35 42 70 105 210 3,923 7,846 11,769 19,615 23,538 27,461 39,230 54,922 58,845 82,383 117,690 137,305 164,766 274,610 411,915 823,830

Collatz Trajectory (237 steps to reach 1)

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

823,830 411,915 1,235,746 617,873 1,853,620 926,810 463,405 1,390,216 695,108 347,554 173,777 521,332 260,666 130,333 391,000 195,500 97,750 48,875 146,626 73,313 219,940 109,970 54,985 164,956 82,478 41,239 123,718 61,859 185,578 92,789 278,368 139,184 69,592 34,796 17,398 8,699 26,098 13,049 39,148 19,574 9,787 29,362 14,681 44,044 22,022 11,011 33,034 16,517 49,552 24,776 12,388 6,194 3,097 9,292 4,646 2,323 6,970 3,485 10,456 5,228

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