793,584

2⁴ × 3³ × 11 × 167

Starting at 793,584, the Collatz iteration reaches 1 after 193 steps. The first transition is 396792; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 11 × 167

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 2,499,840

Proper Divisor Sum 1,706,256

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #793561 ← → #793591

Radix Representation

Decimal	793584
Binary	11000001101111110000 (20 bits)
Octal	0o3015760
Hexadecimal	0xC1BF0

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 11 12 16 18 22 24 27 33 36 44 48 54 66 72 88 99 108 132 144 167 176 198 216 264 297 334 396 432 501 528 594 668 792 1,002 1,188 1,336 1,503 1,584 1,837 2,004 2,376 2,672 3,006 3,674 4,008 4,509 4,752 5,511 6,012 7,348 8,016 9,018 11,022

Collatz Trajectory (193 steps to reach 1)

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

793,584 396,792 198,396 99,198 49,599 148,798 74,399 223,198 111,599 334,798 167,399 502,198 251,099 753,298 376,649 1,129,948 564,974 282,487 847,462 423,731 1,271,194 635,597 1,906,792 953,396 476,698 238,349 715,048 357,524 178,762 89,381 268,144 134,072 67,036 33,518 16,759 50,278 25,139 75,418 37,709 113,128 56,564 28,282 14,141 42,424 21,212 10,606 5,303 15,910 7,955 23,866 11,933 35,800 17,900 8,950 4,475 13,426 6,713 20,140 10,070 5,035

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