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Atlas › Integer Profiles › Node 12,349,106

12,349,106

2 × 7 × 11 × 17 × 53 × 89
Abundant Even Composite

12,349,106 factors as 2 × 7 × 11 × 17 × 53 × 89. Its 64 positive divisors give a proper-divisor sum of 12,845,134, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2 × 7 × 11 × 17 × 53 × 89
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 25,194,240
Proper Divisor Sum 12,845,134
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #12349093 ← → #12349111

Radix Representation

Decimal 12349106
Binary 101111000110111010110010 (24 bits)
Octal 0o57067262
Hexadecimal 0xBC6EB2

Divisor Catalog (60 of 64)

1 2 7 11 14 17 22 34 53 77 89 106 119 154 178 187 238 371 374 583 623 742 901 979 1,166 1,246 1,309 1,513 1,802 1,958 2,618 3,026 4,081 4,717 6,307 6,853 8,162 9,434 9,911 10,591 12,614 13,706 16,643 19,822 21,182 33,019 33,286 51,887 66,038 69,377 80,189 103,774 116,501 138,754 160,378 233,002 363,209 561,323 726,418 882,079

Collatz Trajectory (166 steps to reach 1)

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

12,349,106 6,174,553 18,523,660 9,261,830 4,630,915 13,892,746 6,946,373 20,839,120 10,419,560 5,209,780 2,604,890 1,302,445 3,907,336 1,953,668 976,834 488,417 1,465,252 732,626 366,313 1,098,940 549,470 274,735 824,206 412,103 1,236,310 618,155 1,854,466 927,233 2,781,700 1,390,850 695,425 2,086,276 1,043,138 521,569 1,564,708 782,354 391,177 1,173,532 586,766 293,383 880,150 440,075 1,320,226 660,113 1,980,340 990,170 495,085 1,485,256 742,628 371,314 185,657 556,972 278,486 139,243 417,730 208,865 626,596 313,298 156,649 469,948

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