827,280

2⁴ × 3³ × 5 × 383

827,280 has digital root 9. The neighboring primes are 827269 and 827293; its proper-divisor sum differs from the starting integer by 1,202,400.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 5 × 383

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 2,856,960

Proper Divisor Sum 2,029,680

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #827269 ← → #827293

Radix Representation

Decimal	827280
Binary	11001001111110010000 (20 bits)
Octal	0o3117620
Hexadecimal	0xC9F90

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 36 40 45 48 54 60 72 80 90 108 120 135 144 180 216 240 270 360 383 432 540 720 766 1,080 1,149 1,532 1,915 2,160 2,298 3,064 3,447 3,830 4,596 5,745 6,128 6,894 7,660 9,192 10,341 11,490 13,788 15,320 17,235

Collatz Trajectory (131 steps to reach 1)

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

827,280 413,640 206,820 103,410 51,705 155,116 77,558 38,779 116,338 58,169 174,508 87,254 43,627 130,882 65,441 196,324 98,162 49,081 147,244 73,622 36,811 110,434 55,217 165,652 82,826 41,413 124,240 62,120 31,060 15,530 7,765 23,296 11,648 5,824 2,912 1,456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890

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