27,400,800

2⁵ × 3 × 5² × 7² × 233

27,400,800 factors as 2^5 × 3 × 5^2 × 7^2 × 233. Its 216 positive divisors give a proper-divisor sum of 76,795,656, so this integer is abundant. The Collatz stopping time is 224 steps.

Prime Factor Structure

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

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 216

Divisor Sum (σ) 104,196,456

Proper Divisor Sum 76,795,656

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #27400799 ← → #27400801

Radix Representation

Decimal	27400800
Binary	1101000100001101001100000 (25 bits)
Octal	0o150415140
Hexadecimal	0x1A21A60

Divisor Catalog (60 of 216)

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 70 75 80 84 96 98 100 105 112 120 140 147 150 160 168 175 196 200 210 224 233 240 245 280 294 300 336 350 392 400 420 466

Collatz Trajectory (224 steps to reach 1)

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

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 28,978

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