523,827

3⁴ × 29 × 223

523,827 is odd and not a perfect square. Its factorization is 3^4 × 29 × 223 and its 20 divisors sum to 813,120.

Prime Factor Structure

Factorization String 3^4 × 29 × 223

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 20

Divisor Sum (σ) 813,120

Proper Divisor Sum 289,293

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #523801 ← → #523829

Radix Representation

Decimal	523827
Binary	1111111111000110011 (19 bits)
Octal	0o1777063
Hexadecimal	0x7FE33

Divisor Catalog (20)

1 3 9 27 29 81 87 223 261 669 783 2,007 2,349 6,021 6,467 18,063 19,401 58,203 174,609 523,827

Collatz Trajectory (177 steps to reach 1)

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

523,827 1,571,482 785,741 2,357,224 1,178,612 589,306 294,653 883,960 441,980 220,990 110,495 331,486 165,743 497,230 248,615 745,846 372,923 1,118,770 559,385 1,678,156 839,078 419,539 1,258,618 629,309 1,887,928 943,964 471,982 235,991 707,974 353,987 1,061,962 530,981 1,592,944 796,472 398,236 199,118 99,559 298,678 149,339 448,018 224,009 672,028 336,014 168,007 504,022 252,011 756,034 378,017 1,134,052 567,026 283,513 850,540 425,270 212,635 637,906 318,953 956,860 478,430 239,215 717,646

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