523,320

2³ × 3 × 5 × 7² × 89

523,320 factors as 2^3 × 3 × 5 × 7^2 × 89. Its 96 positive divisors give a proper-divisor sum of 1,323,480, so this integer is abundant. The Collatz stopping time is 164 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 7^2 × 89

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 1,846,800

Proper Divisor Sum 1,323,480

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #523307 ← → #523333

Radix Representation

Decimal	523320
Binary	1111111110000111000 (19 bits)
Octal	0o1776070
Hexadecimal	0x7FC38

Divisor Catalog (60 of 96)

1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 28 30 35 40 42 49 56 60 70 84 89 98 105 120 140 147 168 178 196 210 245 267 280 294 356 392 420 445 490 534 588 623 712 735 840 890 980 1,068 1,176 1,246 1,335 1,470 1,780 1,869 1,960

Collatz Trajectory (164 steps to reach 1)

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

523,320 261,660 130,830 65,415 196,246 98,123 294,370 147,185 441,556 220,778 110,389 331,168 165,584 82,792 41,396 20,698 10,349 31,048 15,524 7,762 3,881 11,644 5,822 2,911 8,734 4,367 13,102 6,551 19,654 9,827 29,482 14,741 44,224 22,112 11,056 5,528 2,764 1,382 691 2,074 1,037 3,112 1,556 778 389 1,168 584 292 146 73 220 110 55 166 83 250 125 376 188 94

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