725,829

3 × 13 × 37 × 503

725,829 factors as 3 × 13 × 37 × 503. Its 16 positive divisors give a proper-divisor sum of 346,683, so this integer is deficient. The Collatz stopping time is 180 steps.

Prime Factor Structure

Factorization String 3 × 13 × 37 × 503

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,072,512

Proper Divisor Sum 346,683

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #725827 ← → #725861

Radix Representation

Decimal	725829
Binary	10110001001101000101 (20 bits)
Octal	0o2611505
Hexadecimal	0xB1345

Divisor Catalog (16)

1 3 13 37 39 111 481 503 1,443 1,509 6,539 18,611 19,617 55,833 241,943 725,829

Collatz Trajectory (180 steps to reach 1)

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

725,829 2,177,488 1,088,744 544,372 272,186 136,093 408,280 204,140 102,070 51,035 153,106 76,553 229,660 114,830 57,415 172,246 86,123 258,370 129,185 387,556 193,778 96,889 290,668 145,334 72,667 218,002 109,001 327,004 163,502 81,751 245,254 122,627 367,882 183,941 551,824 275,912 137,956 68,978 34,489 103,468 51,734 25,867 77,602 38,801 116,404 58,202 29,101 87,304 43,652 21,826 10,913 32,740 16,370 8,185 24,556 12,278 6,139 18,418 9,209 27,628

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