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819,600

24 × 3 × 52 × 683
Abundant Even Composite

819,600 factors as 2^4 × 3 × 5^2 × 683. Its 60 positive divisors give a proper-divisor sum of 1,809,696, so this integer is abundant. The Collatz stopping time is 82 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5^2 × 683
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 2,629,296
Proper Divisor Sum 1,809,696
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #819593 ← → #819607

Radix Representation

Decimal 819600
Binary 11001000000110010000 (20 bits)
Octal 0o3100620
Hexadecimal 0xC8190

Divisor Catalog (60)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 40 48 50 60 75 80 100 120 150 200 240 300 400 600 683 1,200 1,366 2,049 2,732 3,415 4,098 5,464 6,830 8,196 10,245 10,928 13,660 16,392 17,075 20,490 27,320 32,784 34,150 40,980 51,225 54,640 68,300 81,960 102,450 136,600 163,920 204,900 273,200 409,800 819,600

Collatz Trajectory (82 steps to reach 1)

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

819,600 409,800 204,900 102,450 51,225 153,676 76,838 38,419 115,258 57,629 172,888 86,444 43,222 21,611 64,834 32,417 97,252 48,626 24,313 72,940 36,470 18,235 54,706 27,353 82,060 41,030 20,515 61,546 30,773 92,320 46,160 23,080 11,540 5,770 2,885 8,656 4,328 2,164 1,082 541 1,624 812 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148

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