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Atlas › Integer Profiles › Node 8,993,985

8,993,985

3 × 5 × 7 × 11 × 13 × 599
Abundant Odd Composite

8,993,985 factors as 3 × 5 × 7 × 11 × 13 × 599. Its 64 positive divisors give a proper-divisor sum of 10,359,615, so this integer is abundant. The Collatz stopping time is 181 steps.

Prime Factor Structure

Factorization String 3 × 5 × 7 × 11 × 13 × 599
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 19,353,600
Proper Divisor Sum 10,359,615
Digit Sum / Digital Root 51 (Root: 6)
Adjacent Primes #8993981 ← → #8994017

Radix Representation

Decimal 8993985
Binary 100010010011110011000001 (24 bits)
Octal 0o42236301
Hexadecimal 0x893CC1

Divisor Catalog (60 of 64)

1 3 5 7 11 13 15 21 33 35 39 55 65 77 91 105 143 165 195 231 273 385 429 455 599 715 1,001 1,155 1,365 1,797 2,145 2,995 3,003 4,193 5,005 6,589 7,787 8,985 12,579 15,015 19,767 20,965 23,361 32,945 38,935 46,123 54,509 62,895 85,657 98,835 116,805 138,369 163,527 230,615 256,971 272,545 428,285 599,599 691,845 817,635

Collatz Trajectory (181 steps to reach 1)

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

8,993,985 26,981,956 13,490,978 6,745,489 20,236,468 10,118,234 5,059,117 15,177,352 7,588,676 3,794,338 1,897,169 5,691,508 2,845,754 1,422,877 4,268,632 2,134,316 1,067,158 533,579 1,600,738 800,369 2,401,108 1,200,554 600,277 1,800,832 900,416 450,208 225,104 112,552 56,276 28,138 14,069 42,208 21,104 10,552 5,276 2,638 1,319 3,958 1,979 5,938 2,969 8,908 4,454 2,227 6,682 3,341 10,024 5,012 2,506 1,253 3,760 1,880 940 470 235 706 353 1,060 530 265

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