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Atlas › Integer Profiles › Node 27,000,890

27,000,890

2 × 5 × 7 × 499 × 773
Abundant Even Composite

27,000,890 factors as 2 × 5 × 7 × 499 × 773. Its 32 positive divisors give a proper-divisor sum of 28,727,110, so this integer is abundant. The Collatz stopping time is 255 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 499 × 773
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 55,728,000
Proper Divisor Sum 28,727,110
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #27000887 ← → #27000899

Radix Representation

Decimal 27000890
Binary 1100111000000000000111010 (25 bits)
Octal 0o147000072
Hexadecimal 0x19C003A

Divisor Catalog (32)

1 2 5 7 10 14 35 70 499 773 998 1,546 2,495 3,493 3,865 4,990 5,411 6,986 7,730 10,822 17,465 27,055 34,930 54,110 385,727 771,454 1,928,635 2,700,089 3,857,270 5,400,178 13,500,445 27,000,890

Collatz Trajectory (255 steps to reach 1)

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

27,000,890 13,500,445 40,501,336 20,250,668 10,125,334 5,062,667 15,188,002 7,594,001 22,782,004 11,391,002 5,695,501 17,086,504 8,543,252 4,271,626 2,135,813 6,407,440 3,203,720 1,601,860 800,930 400,465 1,201,396 600,698 300,349 901,048 450,524 225,262 112,631 337,894 168,947 506,842 253,421 760,264 380,132 190,066 95,033 285,100 142,550 71,275 213,826 106,913 320,740 160,370 80,185 240,556 120,278 60,139 180,418 90,209 270,628 135,314 67,657 202,972 101,486 50,743 152,230 76,115 228,346 114,173 342,520 171,260

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