27,763,560

2³ × 3⁴ × 5 × 11 × 19 × 41

27,763,560 factors as 2^3 × 3^4 × 5 × 11 × 19 × 41. Its 320 positive divisors give a proper-divisor sum of 82,007,640, so this integer is abundant. The Collatz stopping time is 136 steps.

Prime Factor Structure

Factorization String 2^3 × 3^4 × 5 × 11 × 19 × 41

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 320

Divisor Sum (σ) 109,771,200

Proper Divisor Sum 82,007,640

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #27763543 ← → #27763577

Radix Representation

Decimal	27763560
Binary	1101001111010001101101000 (25 bits)
Octal	0o151721550
Hexadecimal	0x1A7A368

Divisor Catalog (60 of 320)

1 2 3 4 5 6 8 9 10 11 12 15 18 19 20 22 24 27 30 33 36 38 40 41 44 45 54 55 57 60 66 72 76 81 82 88 90 95 99 108 110 114 120 123 132 135 152 162 164 165 171 180 190 198 205 209 216 220 228 246

Collatz Trajectory (136 steps to reach 1)

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

27,763,560 13,881,780 6,940,890 3,470,445 10,411,336 5,205,668 2,602,834 1,301,417 3,904,252 1,952,126 976,063 2,928,190 1,464,095 4,392,286 2,196,143 6,588,430 3,294,215 9,882,646 4,941,323 14,823,970 7,411,985 22,235,956 11,117,978 5,558,989 16,676,968 8,338,484 4,169,242 2,084,621 6,253,864 3,126,932 1,563,466 781,733 2,345,200 1,172,600 586,300 293,150 146,575 439,726 219,863 659,590 329,795 989,386 494,693 1,484,080 742,040 371,020 185,510 92,755 278,266 139,133 417,400 208,700 104,350 52,175 156,526 78,263 234,790 117,395 352,186 176,093

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