729,648

2⁴ × 3⁴ × 563

729,648 is even and not a perfect square. Its factorization is 2^4 × 3^4 × 563 and its 50 divisors sum to 2,115,564.

Prime Factor Structure

Factorization String 2^4 × 3^4 × 563

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 50

Divisor Sum (σ) 2,115,564

Proper Divisor Sum 1,385,916

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #729643 ← → #729649

Radix Representation

Decimal	729648
Binary	10110010001000110000 (20 bits)
Octal	0o2621060
Hexadecimal	0xB2230

Divisor Catalog (50)

1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72 81 108 144 162 216 324 432 563 648 1,126 1,296 1,689 2,252 3,378 4,504 5,067 6,756 9,008 10,134 13,512 15,201 20,268 27,024 30,402 40,536 45,603 60,804 81,072 91,206 121,608 182,412 243,216 364,824 729,648

Collatz Trajectory (74 steps to reach 1)

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

729,648 364,824 182,412 91,206 45,603 136,810 68,405 205,216 102,608 51,304 25,652 12,826 6,413 19,240 9,620 4,810 2,405 7,216 3,608 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382 191 574 287 862 431 1,294 647 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22

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