36,080,800

2⁵ × 5² × 7 × 17 × 379

36,080,800 factors as 2^5 × 5^2 × 7 × 17 × 379. Its 144 positive divisors give a proper-divisor sum of 70,787,360, so this integer is abundant. The Collatz stopping time is 90 steps.

Prime Factor Structure

Factorization String 2^5 × 5^2 × 7 × 17 × 379

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 106,868,160

Proper Divisor Sum 70,787,360

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #36080743 ← → #36080839

Radix Representation

Decimal	36080800
Binary	10001001101000110010100000 (26 bits)
Octal	0o211506240
Hexadecimal	0x2268CA0

Divisor Catalog (60 of 144)

1 2 4 5 7 8 10 14 16 17 20 25 28 32 34 35 40 50 56 68 70 80 85 100 112 119 136 140 160 170 175 200 224 238 272 280 340 350 379 400 425 476 544 560 595 680 700 758 800 850 952 1,120 1,190 1,360 1,400 1,516 1,700 1,895 1,904 2,380

Collatz Trajectory (90 steps to reach 1)

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

36,080,800 18,040,400 9,020,200 4,510,100 2,255,050 1,127,525 3,382,576 1,691,288 845,644 422,822 211,411 634,234 317,117 951,352 475,676 237,838 118,919 356,758 178,379 535,138 267,569 802,708 401,354 200,677 602,032 301,016 150,508 75,254 37,627 112,882 56,441 169,324 84,662 42,331 126,994 63,497 190,492 95,246 47,623 142,870 71,435 214,306 107,153 321,460 160,730 80,365 241,096 120,548 60,274 30,137 90,412 45,206 22,603 67,810 33,905 101,716 50,858 25,429 76,288 38,144

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