54,009,760

2⁵ × 5 × 7² × 83²

54,009,760 factors as 2^5 × 5 × 7^2 × 83^2. Its 108 positive divisors give a proper-divisor sum of 96,230,498, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 7^2 × 83^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 108

Divisor Sum (σ) 150,240,258

Proper Divisor Sum 96,230,498

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #54009757 ← → #54009779

Radix Representation

Decimal	54009760
Binary	11001110000001111110100000 (26 bits)
Octal	0o316017640
Hexadecimal	0x3381FA0

Divisor Catalog (60 of 108)

1 2 4 5 7 8 10 14 16 20 28 32 35 40 49 56 70 80 83 98 112 140 160 166 196 224 245 280 332 392 415 490 560 581 664 784 830 980 1,120 1,162 1,328 1,568 1,660 1,960 2,324 2,656 2,905 3,320 3,920 4,067 4,648 5,810 6,640 6,889 7,840 8,134 9,296 11,620 13,280 13,778

Collatz Trajectory (137 steps to reach 1)

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

54,009,760 27,004,880 13,502,440 6,751,220 3,375,610 1,687,805 5,063,416 2,531,708 1,265,854 632,927 1,898,782 949,391 2,848,174 1,424,087 4,272,262 2,136,131 6,408,394 3,204,197 9,612,592 4,806,296 2,403,148 1,201,574 600,787 1,802,362 901,181 2,703,544 1,351,772 675,886 337,943 1,013,830 506,915 1,520,746 760,373 2,281,120 1,140,560 570,280 285,140 142,570 71,285 213,856 106,928 53,464 26,732 13,366 6,683 20,050 10,025 30,076 15,038 7,519 22,558 11,279 33,838 16,919 50,758 25,379 76,138 38,069 114,208 57,104

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