λ
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Atlas › Integer Profiles › Node 450,792

450,792

23 × 33 × 2087
Abundant Even Composite

450,792 factors as 2^3 × 3^3 × 2087. Its 32 positive divisors give a proper-divisor sum of 802,008, so this integer is abundant. The Collatz stopping time is 63 steps.

Prime Factor Structure

Factorization String 2^3 × 3^3 × 2087
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 1,252,800
Proper Divisor Sum 802,008
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #450787 ← → #450797

Radix Representation

Decimal 450792
Binary 1101110000011101000 (19 bits)
Octal 0o1560350
Hexadecimal 0x6E0E8

Divisor Catalog (32)

1 2 3 4 6 8 9 12 18 24 27 36 54 72 108 216 2,087 4,174 6,261 8,348 12,522 16,696 18,783 25,044 37,566 50,088 56,349 75,132 112,698 150,264 225,396 450,792

Collatz Trajectory (63 steps to reach 1)

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

450,792 225,396 112,698 56,349 169,048 84,524 42,262 21,131 63,394 31,697 95,092 47,546 23,773 71,320 35,660 17,830 8,915 26,746 13,373 40,120 20,060 10,030 5,015 15,046 7,523 22,570 11,285 33,856 16,928 8,464 4,232 2,116 1,058 529 1,588 794 397 1,192 596 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16

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