33,765,120

2⁸ × 3³ × 5 × 977

33,765,120 factors as 2^8 × 3^3 × 5 × 977. Its 144 positive divisors give a proper-divisor sum of 86,176,800, so this integer is abundant. The Collatz stopping time is 108 steps.

Prime Factor Structure

Factorization String 2^8 × 3^3 × 5 × 977

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 119,941,920

Proper Divisor Sum 86,176,800

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #33765103 ← → #33765133

Radix Representation

Decimal	33765120
Binary	10000000110011011100000000 (26 bits)
Octal	0o200633400
Hexadecimal	0x2033700

Divisor Catalog (60 of 144)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 64 72 80 90 96 108 120 128 135 144 160 180 192 216 240 256 270 288 320 360 384 432 480 540 576 640 720 768 864 960 977 1,080 1,152 1,280 1,440 1,728

Collatz Trajectory (108 steps to reach 1)

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

33,765,120 16,882,560 8,441,280 4,220,640 2,110,320 1,055,160 527,580 263,790 131,895 395,686 197,843 593,530 296,765 890,296 445,148 222,574 111,287 333,862 166,931 500,794 250,397 751,192 375,596 187,798 93,899 281,698 140,849 422,548 211,274 105,637 316,912 158,456 79,228 39,614 19,807 59,422 29,711 89,134 44,567 133,702 66,851 200,554 100,277 300,832 150,416 75,208 37,604 18,802 9,401 28,204 14,102 7,051 21,154 10,577 31,732 15,866 7,933 23,800 11,900 5,950

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