211,757

7 × 13² × 179

211,757 factors as 7 × 13^2 × 179. Its 12 positive divisors give a proper-divisor sum of 51,763, so this integer is deficient. The Collatz stopping time is 80 steps.

Prime Factor Structure

Factorization String 7 × 13^2 × 179

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 263,520

Proper Divisor Sum 51,763

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #211747 ← → #211777

Radix Representation

Decimal	211757
Binary	110011101100101101 (18 bits)
Octal	0o635455
Hexadecimal	0x33B2D

Divisor Catalog (12)

1 7 13 91 169 179 1,183 1,253 2,327 16,289 30,251 211,757

Collatz Trajectory (80 steps to reach 1)

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

211,757 635,272 317,636 158,818 79,409 238,228 119,114 59,557 178,672 89,336 44,668 22,334 11,167 33,502 16,751 50,254 25,127 75,382 37,691 113,074 56,537 169,612 84,806 42,403 127,210 63,605 190,816 95,408 47,704 23,852 11,926 5,963 17,890 8,945 26,836 13,418 6,709 20,128 10,064 5,032 2,516 1,258 629 1,888 944 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38

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