688,086

2 × 3² × 7 × 43 × 127

688,086 factors as 2 × 3^2 × 7 × 43 × 127. Its 48 positive divisors give a proper-divisor sum of 1,069,098, so this integer is abundant. The Collatz stopping time is 198 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 7 × 43 × 127

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,757,184

Proper Divisor Sum 1,069,098

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #688073 ← → #688087

Radix Representation

Decimal	688086
Binary	10100111111111010110 (20 bits)
Octal	0o2477726
Hexadecimal	0xA7FD6

Divisor Catalog (48)

1 2 3 6 7 9 14 18 21 42 43 63 86 126 127 129 254 258 301 381 387 602 762 774 889 903 1,143 1,778 1,806 2,286 2,667 2,709 5,334 5,418 5,461 8,001 10,922 16,002 16,383 32,766 38,227 49,149 76,454 98,298 114,681 229,362 344,043 688,086

Collatz Trajectory (198 steps to reach 1)

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

688,086 344,043 1,032,130 516,065 1,548,196 774,098 387,049 1,161,148 580,574 290,287 870,862 435,431 1,306,294 653,147 1,959,442 979,721 2,939,164 1,469,582 734,791 2,204,374 1,102,187 3,306,562 1,653,281 4,959,844 2,479,922 1,239,961 3,719,884 1,859,942 929,971 2,789,914 1,394,957 4,184,872 2,092,436 1,046,218 523,109 1,569,328 784,664 392,332 196,166 98,083 294,250 147,125 441,376 220,688 110,344 55,172 27,586 13,793 41,380 20,690 10,345 31,036 15,518 7,759 23,278 11,639 34,918 17,459 52,378 26,189

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