180,891

3² × 101 × 199

180,891 factors as 3^2 × 101 × 199. Its 12 positive divisors give a proper-divisor sum of 84,309, so this integer is deficient. The Collatz stopping time is 116 steps.

Prime Factor Structure

Factorization String 3^2 × 101 × 199

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 265,200

Proper Divisor Sum 84,309

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #180883 ← → #180907

Radix Representation

Decimal	180891
Binary	101100001010011011 (18 bits)
Octal	0o541233
Hexadecimal	0x2C29B

Divisor Catalog (12)

1 3 9 101 199 303 597 909 1,791 20,099 60,297 180,891

Collatz Trajectory (116 steps to reach 1)

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

180,891 542,674 271,337 814,012 407,006 203,503 610,510 305,255 915,766 457,883 1,373,650 686,825 2,060,476 1,030,238 515,119 1,545,358 772,679 2,318,038 1,159,019 3,477,058 1,738,529 5,215,588 2,607,794 1,303,897 3,911,692 1,955,846 977,923 2,933,770 1,466,885 4,400,656 2,200,328 1,100,164 550,082 275,041 825,124 412,562 206,281 618,844 309,422 154,711 464,134 232,067 696,202 348,101 1,044,304 522,152 261,076 130,538 65,269 195,808 97,904 48,952 24,476 12,238 6,119 18,358 9,179 27,538 13,769 41,308

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