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728,560

24 × 5 × 7 × 1301
Abundant Even Composite

728,560 factors as 2^4 × 5 × 7 × 1301. Its 40 positive divisors give a proper-divisor sum of 1,208,816, so this integer is abundant. The Collatz stopping time is 87 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 1301
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 1,937,376
Proper Divisor Sum 1,208,816
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #728557 ← → #728561

Radix Representation

Decimal 728560
Binary 10110001110111110000 (20 bits)
Octal 0o2616760
Hexadecimal 0xB1DF0

Divisor Catalog (40)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 280 560 1,301 2,602 5,204 6,505 9,107 10,408 13,010 18,214 20,816 26,020 36,428 45,535 52,040 72,856 91,070 104,080 145,712 182,140 364,280 728,560

Collatz Trajectory (87 steps to reach 1)

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

728,560 364,280 182,140 91,070 45,535 136,606 68,303 204,910 102,455 307,366 153,683 461,050 230,525 691,576 345,788 172,894 86,447 259,342 129,671 389,014 194,507 583,522 291,761 875,284 437,642 218,821 656,464 328,232 164,116 82,058 41,029 123,088 61,544 30,772 15,386 7,693 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

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