32,093,600

2⁵ × 5² × 7 × 11 × 521

32,093,600 factors as 2^5 × 5^2 × 7 × 11 × 521. Its 144 positive divisors give a proper-divisor sum of 65,775,136, so this integer is abundant. The Collatz stopping time is 188 steps.

Prime Factor Structure

Factorization String 2^5 × 5^2 × 7 × 11 × 521

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 97,868,736

Proper Divisor Sum 65,775,136

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #32093591 ← → #32093617

Radix Representation

Decimal	32093600
Binary	1111010011011010110100000 (25 bits)
Octal	0o172332640
Hexadecimal	0x1E9B5A0

Divisor Catalog (60 of 144)

1 2 4 5 7 8 10 11 14 16 20 22 25 28 32 35 40 44 50 55 56 70 77 80 88 100 110 112 140 154 160 175 176 200 220 224 275 280 308 350 352 385 400 440 521 550 560 616 700 770 800 880 1,042 1,100 1,120 1,232 1,400 1,540 1,760 1,925

Collatz Trajectory (188 steps to reach 1)

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

32,093,600 16,046,800 8,023,400 4,011,700 2,005,850 1,002,925 3,008,776 1,504,388 752,194 376,097 1,128,292 564,146 282,073 846,220 423,110 211,555 634,666 317,333 952,000 476,000 238,000 119,000 59,500 29,750 14,875 44,626 22,313 66,940 33,470 16,735 50,206 25,103 75,310 37,655 112,966 56,483 169,450 84,725 254,176 127,088 63,544 31,772 15,886 7,943 23,830 11,915 35,746 17,873 53,620 26,810 13,405 40,216 20,108 10,054 5,027 15,082 7,541 22,624 11,312 5,656

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