54,801,600

2⁶ × 3 × 5² × 7² × 233

54,801,600 factors as 2^6 × 3 × 5^2 × 7^2 × 233. Its 252 positive divisors give a proper-divisor sum of 155,245,224, so this integer is abundant. The Collatz stopping time is 225 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 5^2 × 7^2 × 233

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 252

Divisor Sum (σ) 210,046,824

Proper Divisor Sum 155,245,224

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #54801599 ← → #54801601

Radix Representation

Decimal	54801600
Binary	11010001000011010011000000 (26 bits)
Octal	0o321032300
Hexadecimal	0x34434C0

Divisor Catalog (60 of 252)

1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 25 28 30 32 35 40 42 48 49 50 56 60 64 70 75 80 84 96 98 100 105 112 120 140 147 150 160 168 175 192 196 200 210 224 233 240 245 280 294 300 320 336 350 392

Collatz Trajectory (225 steps to reach 1)

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

54,801,600 27,400,800 13,700,400 6,850,200 3,425,100 1,712,550 856,275 2,568,826 1,284,413 3,853,240 1,926,620 963,310 481,655 1,444,966 722,483 2,167,450 1,083,725 3,251,176 1,625,588 812,794 406,397 1,219,192 609,596 304,798 152,399 457,198 228,599 685,798 342,899 1,028,698 514,349 1,543,048 771,524 385,762 192,881 578,644 289,322 144,661 433,984 216,992 108,496 54,248 27,124 13,562 6,781 20,344 10,172 5,086 2,543 7,630 3,815 11,446 5,723 17,170 8,585 25,756 12,878 6,439 19,318 9,659

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