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Atlas › Integer Profiles › Node 2,088,080

2,088,080

24 × 5 × 43 × 607
Abundant Even Composite

2,088,080 factors as 2^4 × 5 × 43 × 607. Its 40 positive divisors give a proper-divisor sum of 2,887,792, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 43 × 607
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 4,975,872
Proper Divisor Sum 2,887,792
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #2088077 ← → #2088103

Radix Representation

Decimal 2088080
Binary 111111101110010010000 (21 bits)
Octal 0o7756220
Hexadecimal 0x1FDC90

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 43 80 86 172 215 344 430 607 688 860 1,214 1,720 2,428 3,035 3,440 4,856 6,070 9,712 12,140 24,280 26,101 48,560 52,202 104,404 130,505 208,808 261,010 417,616 522,020 1,044,040 2,088,080

Collatz Trajectory (135 steps to reach 1)

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

2,088,080 1,044,040 522,020 261,010 130,505 391,516 195,758 97,879 293,638 146,819 440,458 220,229 660,688 330,344 165,172 82,586 41,293 123,880 61,940 30,970 15,485 46,456 23,228 11,614 5,807 17,422 8,711 26,134 13,067 39,202 19,601 58,804 29,402 14,701 44,104 22,052 11,026 5,513 16,540 8,270 4,135 12,406 6,203 18,610 9,305 27,916 13,958 6,979 20,938 10,469 31,408 15,704 7,852 3,926 1,963 5,890 2,945 8,836 4,418 2,209

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