12,823,328

2⁵ × 7 × 19 × 23 × 131

12,823,328 factors as 2^5 × 7 × 19 × 23 × 131. Its 96 positive divisors give a proper-divisor sum of 19,110,112, so this integer is abundant. The Collatz stopping time is 78 steps.

Prime Factor Structure

Factorization String 2^5 × 7 × 19 × 23 × 131

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 31,933,440

Proper Divisor Sum 19,110,112

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #12823319 ← → #12823333

Radix Representation

Decimal	12823328
Binary	110000111010101100100000 (24 bits)
Octal	0o60725440
Hexadecimal	0xC3AB20

Divisor Catalog (60 of 96)

1 2 4 7 8 14 16 19 23 28 32 38 46 56 76 92 112 131 133 152 161 184 224 262 266 304 322 368 437 524 532 608 644 736 874 917 1,048 1,064 1,288 1,748 1,834 2,096 2,128 2,489 2,576 3,013 3,059 3,496 3,668 4,192 4,256 4,978 5,152 6,026 6,118 6,992 7,336 9,956 12,052 12,236

Collatz Trajectory (78 steps to reach 1)

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

12,823,328 6,411,664 3,205,832 1,602,916 801,458 400,729 1,202,188 601,094 300,547 901,642 450,821 1,352,464 676,232 338,116 169,058 84,529 253,588 126,794 63,397 190,192 95,096 47,548 23,774 11,887 35,662 17,831 53,494 26,747 80,242 40,121 120,364 60,182 30,091 90,274 45,137 135,412 67,706 33,853 101,560 50,780 25,390 12,695 38,086 19,043 57,130 28,565 85,696 42,848 21,424 10,712 5,356 2,678 1,339 4,018 2,009 6,028 3,014 1,507 4,522 2,261

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