829,980

2² × 3³ × 5 × 29 × 53

829,980 factors as 2^2 × 3^3 × 5 × 29 × 53. Its 96 positive divisors give a proper-divisor sum of 1,891,620, so this integer is abundant. The Collatz stopping time is 175 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 5 × 29 × 53

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 2,721,600

Proper Divisor Sum 1,891,620

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #829979 ← → #829987

Radix Representation

Decimal	829980
Binary	11001010101000011100 (20 bits)
Octal	0o3125034
Hexadecimal	0xCAA1C

Divisor Catalog (60 of 96)

1 2 3 4 5 6 9 10 12 15 18 20 27 29 30 36 45 53 54 58 60 87 90 106 108 116 135 145 159 174 180 212 261 265 270 290 318 348 435 477 522 530 540 580 636 783 795 870 954 1,044 1,060 1,305 1,431 1,537 1,566 1,590 1,740 1,908 2,385 2,610

Collatz Trajectory (175 steps to reach 1)

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

829,980 414,990 207,495 622,486 311,243 933,730 466,865 1,400,596 700,298 350,149 1,050,448 525,224 262,612 131,306 65,653 196,960 98,480 49,240 24,620 12,310 6,155 18,466 9,233 27,700 13,850 6,925 20,776 10,388 5,194 2,597 7,792 3,896 1,948 974 487 1,462 731 2,194 1,097 3,292 1,646 823 2,470 1,235 3,706 1,853 5,560 2,780 1,390 695 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587 1,762 881

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