729,630

2 × 3² × 5 × 11² × 67

729,630 factors as 2 × 3^2 × 5 × 11^2 × 67. Its 72 positive divisors give a proper-divisor sum of 1,386,666, so this integer is abundant. The Collatz stopping time is 180 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 11^2 × 67

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,116,296

Proper Divisor Sum 1,386,666

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #729613 ← → #729637

Radix Representation

Decimal	729630
Binary	10110010001000011110 (20 bits)
Octal	0o2621036
Hexadecimal	0xB221E

Divisor Catalog (60 of 72)

1 2 3 5 6 9 10 11 15 18 22 30 33 45 55 66 67 90 99 110 121 134 165 198 201 242 330 335 363 402 495 603 605 670 726 737 990 1,005 1,089 1,206 1,210 1,474 1,815 2,010 2,178 2,211 3,015 3,630 3,685 4,422 5,445 6,030 6,633 7,370 8,107 10,890 11,055 13,266 16,214 22,110

Collatz Trajectory (180 steps to reach 1)

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

729,630 364,815 1,094,446 547,223 1,641,670 820,835 2,462,506 1,231,253 3,693,760 1,846,880 923,440 461,720 230,860 115,430 57,715 173,146 86,573 259,720 129,860 64,930 32,465 97,396 48,698 24,349 73,048 36,524 18,262 9,131 27,394 13,697 41,092 20,546 10,273 30,820 15,410 7,705 23,116 11,558 5,779 17,338 8,669 26,008 13,004 6,502 3,251 9,754 4,877 14,632 7,316 3,658 1,829 5,488 2,744 1,372 686 343 1,030 515 1,546 773

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