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Atlas › Integer Profiles › Node 80,937,828

80,937,828

22 × 32 × 23 × 239 × 409
Abundant Even Composite

80,937,828 factors as 2^2 × 3^2 × 23 × 239 × 409. Its 72 positive divisors give a proper-divisor sum of 133,967,772, so this integer is abundant. The Collatz stopping time is 109 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 23 × 239 × 409
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 214,905,600
Proper Divisor Sum 133,967,772
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #80937827 ← → #80937839

Radix Representation

Decimal 80937828
Binary 100110100110000001101100100 (27 bits)
Octal 0o464601544
Hexadecimal 0x4D30364

Divisor Catalog (60 of 72)

1 2 3 4 6 9 12 18 23 36 46 69 92 138 207 239 276 409 414 478 717 818 828 956 1,227 1,434 1,636 2,151 2,454 2,868 3,681 4,302 4,908 5,497 7,362 8,604 9,407 10,994 14,724 16,491 18,814 21,988 28,221 32,982 37,628 49,473 56,442 65,964 84,663 97,751 98,946 112,884 169,326 195,502 197,892 293,253 338,652 391,004 586,506 879,759

Collatz Trajectory (109 steps to reach 1)

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

80,937,828 40,468,914 20,234,457 60,703,372 30,351,686 15,175,843 45,527,530 22,763,765 68,291,296 34,145,648 17,072,824 8,536,412 4,268,206 2,134,103 6,402,310 3,201,155 9,603,466 4,801,733 14,405,200 7,202,600 3,601,300 1,800,650 900,325 2,700,976 1,350,488 675,244 337,622 168,811 506,434 253,217 759,652 379,826 189,913 569,740 284,870 142,435 427,306 213,653 640,960 320,480 160,240 80,120 40,060 20,030 10,015 30,046 15,023 45,070 22,535 67,606 33,803 101,410 50,705 152,116 76,058 38,029 114,088 57,044 28,522 14,261

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