83,358

2 × 3² × 11 × 421

83,358 factors as 2 × 3^2 × 11 × 421. Its 24 positive divisors give a proper-divisor sum of 114,138, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 11 × 421

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 197,496

Proper Divisor Sum 114,138

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #83357 ← → #83383

Radix Representation

Decimal	83358
Binary	10100010110011110 (17 bits)
Octal	0o242636
Hexadecimal	0x1459E

Divisor Catalog (24)

1 2 3 6 9 11 18 22 33 66 99 198 421 842 1,263 2,526 3,789 4,631 7,578 9,262 13,893 27,786 41,679 83,358

Collatz Trajectory (138 steps to reach 1)

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

83,358 41,679 125,038 62,519 187,558 93,779 281,338 140,669 422,008 211,004 105,502 52,751 158,254 79,127 237,382 118,691 356,074 178,037 534,112 267,056 133,528 66,764 33,382 16,691 50,074 25,037 75,112 37,556 18,778 9,389 28,168 14,084 7,042 3,521 10,564 5,282 2,641 7,924 3,962 1,981 5,944 2,972 1,486 743 2,230 1,115 3,346 1,673 5,020 2,510 1,255 3,766 1,883 5,650 2,825 8,476 4,238 2,119 6,358 3,179

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