585,600

2⁷ × 3 × 5² × 61

585,600 is even and not a perfect square. Its factorization is 2^7 × 3 × 5^2 × 61 and its 96 divisors sum to 1,960,440.

Prime Factor Structure

Factorization String 2^7 × 3 × 5^2 × 61

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 1,960,440

Proper Divisor Sum 1,374,840

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #585593 ← → #585601

Radix Representation

Decimal	585600
Binary	10001110111110000000 (20 bits)
Octal	0o2167600
Hexadecimal	0x8EF80

Divisor Catalog (60 of 96)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 32 40 48 50 60 61 64 75 80 96 100 120 122 128 150 160 183 192 200 240 244 300 305 320 366 384 400 480 488 600 610 640 732 800 915 960 976 1,200 1,220 1,464 1,525 1,600 1,830 1,920 1,952

Collatz Trajectory (128 steps to reach 1)

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

585,600 292,800 146,400 73,200 36,600 18,300 9,150 4,575 13,726 6,863 20,590 10,295 30,886 15,443 46,330 23,165 69,496 34,748 17,374 8,687 26,062 13,031 39,094 19,547 58,642 29,321 87,964 43,982 21,991 65,974 32,987 98,962 49,481 148,444 74,222 37,111 111,334 55,667 167,002 83,501 250,504 125,252 62,626 31,313 93,940 46,970 23,485 70,456 35,228 17,614 8,807 26,422 13,211 39,634 19,817 59,452 29,726 14,863 44,590 22,295

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