724,920

2³ × 3 × 5 × 7 × 863

724,920 factors as 2^3 × 3 × 5 × 7 × 863. Its 64 positive divisors give a proper-divisor sum of 1,763,400, so this integer is abundant. The Collatz stopping time is 180 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 7 × 863

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 2,488,320

Proper Divisor Sum 1,763,400

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #724903 ← → #724939

Radix Representation

Decimal	724920
Binary	10110000111110111000 (20 bits)
Octal	0o2607670
Hexadecimal	0xB0FB8

Divisor Catalog (60 of 64)

1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 28 30 35 40 42 56 60 70 84 105 120 140 168 210 280 420 840 863 1,726 2,589 3,452 4,315 5,178 6,041 6,904 8,630 10,356 12,082 12,945 17,260 18,123 20,712 24,164 25,890 30,205 34,520 36,246 48,328 51,780 60,410 72,492 90,615 103,560 120,820 144,984

Collatz Trajectory (180 steps to reach 1)

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

724,920 362,460 181,230 90,615 271,846 135,923 407,770 203,885 611,656 305,828 152,914 76,457 229,372 114,686 57,343 172,030 86,015 258,046 129,023 387,070 193,535 580,606 290,303 870,910 435,455 1,306,366 653,183 1,959,550 979,775 2,939,326 1,469,663 4,408,990 2,204,495 6,613,486 3,306,743 9,920,230 4,960,115 14,880,346 7,440,173 22,320,520 11,160,260 5,580,130 2,790,065 8,370,196 4,185,098 2,092,549 6,277,648 3,138,824 1,569,412 784,706 392,353 1,177,060 588,530 294,265 882,796 441,398 220,699 662,098 331,049 993,148

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