852,852

2² × 3 × 7 × 11 × 13 × 71

852,852 factors as 2^2 × 3 × 7 × 11 × 13 × 71. Its 96 positive divisors give a proper-divisor sum of 1,856,652, so this integer is abundant. The Collatz stopping time is 82 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 11 × 13 × 71

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 2,709,504

Proper Divisor Sum 1,856,652

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #852851 ← → #852857

Radix Representation

Decimal	852852
Binary	11010000001101110100 (20 bits)
Octal	0o3201564
Hexadecimal	0xD0374

Divisor Catalog (60 of 96)

1 2 3 4 6 7 11 12 13 14 21 22 26 28 33 39 42 44 52 66 71 77 78 84 91 132 142 143 154 156 182 213 231 273 284 286 308 364 426 429 462 497 546 572 781 852 858 923 924 994 1,001 1,092 1,491 1,562 1,716 1,846 1,988 2,002 2,343 2,769

Collatz Trajectory (82 steps to reach 1)

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

852,852 426,426 213,213 639,640 319,820 159,910 79,955 239,866 119,933 359,800 179,900 89,950 44,975 134,926 67,463 202,390 101,195 303,586 151,793 455,380 227,690 113,845 341,536 170,768 85,384 42,692 21,346 10,673 32,020 16,010 8,005 24,016 12,008 6,004 3,002 1,501 4,504 2,252 1,126 563 1,690 845 2,536 1,268 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152

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