529,980

2² × 3 × 5 × 11² × 73

529,980 factors as 2^2 × 3 × 5 × 11^2 × 73. Its 72 positive divisors give a proper-divisor sum of 1,123,476, so this integer is abundant. The Collatz stopping time is 102 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 11^2 × 73

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 1,653,456

Proper Divisor Sum 1,123,476

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #529979 ← → #529981

Radix Representation

Decimal	529980
Binary	10000001011000111100 (20 bits)
Octal	0o2013074
Hexadecimal	0x8163C

Divisor Catalog (60 of 72)

1 2 3 4 5 6 10 11 12 15 20 22 30 33 44 55 60 66 73 110 121 132 146 165 219 220 242 292 330 363 365 438 484 605 660 726 730 803 876 1,095 1,210 1,452 1,460 1,606 1,815 2,190 2,409 2,420 3,212 3,630 4,015 4,380 4,818 7,260 8,030 8,833 9,636 12,045 16,060 17,666

Collatz Trajectory (102 steps to reach 1)

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

529,980 264,990 132,495 397,486 198,743 596,230 298,115 894,346 447,173 1,341,520 670,760 335,380 167,690 83,845 251,536 125,768 62,884 31,442 15,721 47,164 23,582 11,791 35,374 17,687 53,062 26,531 79,594 39,797 119,392 59,696 29,848 14,924 7,462 3,731 11,194 5,597 16,792 8,396 4,198 2,099 6,298 3,149 9,448 4,724 2,362 1,181 3,544 1,772 886 443 1,330 665 1,996 998 499 1,498 749 2,248 1,124 562

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