709,688

2³ × 7 × 19 × 23 × 29

Starting at 709,688, the Collatz iteration reaches 1 after 211 steps. The first transition is 354844; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 7 × 19 × 23 × 29

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 1,728,000

Proper Divisor Sum 1,018,312

Digit Sum / Digital Root 38 (Root: 2)

Adjacent Primes #709679 ← → #709691

Radix Representation

Decimal	709688
Binary	10101101010000111000 (20 bits)
Octal	0o2552070
Hexadecimal	0xAD438

Divisor Catalog (60 of 64)

1 2 4 7 8 14 19 23 28 29 38 46 56 58 76 92 116 133 152 161 184 203 232 266 322 406 437 532 551 644 667 812 874 1,064 1,102 1,288 1,334 1,624 1,748 2,204 2,668 3,059 3,496 3,857 4,408 4,669 5,336 6,118 7,714 9,338 12,236 12,673 15,428 18,676 24,472 25,346 30,856 37,352 50,692 88,711

Collatz Trajectory (211 steps to reach 1)

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

709,688 354,844 177,422 88,711 266,134 133,067 399,202 199,601 598,804 299,402 149,701 449,104 224,552 112,276 56,138 28,069 84,208 42,104 21,052 10,526 5,263 15,790 7,895 23,686 11,843 35,530 17,765 53,296 26,648 13,324 6,662 3,331 9,994 4,997 14,992 7,496 3,748 1,874 937 2,812 1,406 703 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690 5,345 16,036 8,018 4,009 12,028 6,014 3,007 9,022 4,511

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