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Atlas › Integer Profiles › Node 12,810,688

12,810,688

26 × 11 × 31 × 587
Abundant Even Composite

12,810,688 factors as 2^6 × 11 × 31 × 587. Its 56 positive divisors give a proper-divisor sum of 15,864,896, so this integer is abundant. The Collatz stopping time is 96 steps.

Prime Factor Structure

Factorization String 2^6 × 11 × 31 × 587
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 28,675,584
Proper Divisor Sum 15,864,896
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #12810667 ← → #12810709

Radix Representation

Decimal 12810688
Binary 110000110111100111000000 (24 bits)
Octal 0o60674700
Hexadecimal 0xC379C0

Divisor Catalog (56)

1 2 4 8 11 16 22 31 32 44 62 64 88 124 176 248 341 352 496 587 682 704 992 1,174 1,364 1,984 2,348 2,728 4,696 5,456 6,457 9,392 10,912 12,914 18,197 18,784 21,824 25,828 36,394 37,568 51,656 72,788 103,312 145,576 200,167 206,624 291,152 400,334 413,248 582,304 800,668 1,164,608 1,601,336 3,202,672 6,405,344 12,810,688

Collatz Trajectory (96 steps to reach 1)

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

12,810,688 6,405,344 3,202,672 1,601,336 800,668 400,334 200,167 600,502 300,251 900,754 450,377 1,351,132 675,566 337,783 1,013,350 506,675 1,520,026 760,013 2,280,040 1,140,020 570,010 285,005 855,016 427,508 213,754 106,877 320,632 160,316 80,158 40,079 120,238 60,119 180,358 90,179 270,538 135,269 405,808 202,904 101,452 50,726 25,363 76,090 38,045 114,136 57,068 28,534 14,267 42,802 21,401 64,204 32,102 16,051 48,154 24,077 72,232 36,116 18,058 9,029 27,088 13,544

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