27,816,250

2 × 5⁴ × 7 × 11 × 17²

27,816,250 factors as 2 × 5^4 × 7 × 11 × 17^2. Its 120 positive divisors give a proper-divisor sum of 41,236,646, so this integer is abundant. The Collatz stopping time is 193 steps.

Prime Factor Structure

Factorization String 2 × 5^4 × 7 × 11 × 17^2

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 69,052,896

Proper Divisor Sum 41,236,646

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #27816241 ← → #27816251

Radix Representation

Decimal	27816250
Binary	1101010000111000100111010 (25 bits)
Octal	0o152070472
Hexadecimal	0x1A8713A

Divisor Catalog (60 of 120)

1 2 5 7 10 11 14 17 22 25 34 35 50 55 70 77 85 110 119 125 154 170 175 187 238 250 275 289 350 374 385 425 550 578 595 625 770 850 875 935 1,190 1,250 1,309 1,375 1,445 1,750 1,870 1,925 2,023 2,125 2,618 2,750 2,890 2,975 3,179 3,850 4,046 4,250 4,375 4,675

Collatz Trajectory (193 steps to reach 1)

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

27,816,250 13,908,125 41,724,376 20,862,188 10,431,094 5,215,547 15,646,642 7,823,321 23,469,964 11,734,982 5,867,491 17,602,474 8,801,237 26,403,712 13,201,856 6,600,928 3,300,464 1,650,232 825,116 412,558 206,279 618,838 309,419 928,258 464,129 1,392,388 696,194 348,097 1,044,292 522,146 261,073 783,220 391,610 195,805 587,416 293,708 146,854 73,427 220,282 110,141 330,424 165,212 82,606 41,303 123,910 61,955 185,866 92,933 278,800 139,400 69,700 34,850 17,425 52,276 26,138 13,069 39,208 19,604 9,802 4,901

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