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Atlas › Integer Profiles › Node 54,001,780

54,001,780

22 × 5 × 7 × 499 × 773
Abundant Even Composite

54,001,780 factors as 2^2 × 5 × 7 × 499 × 773. Its 48 positive divisors give a proper-divisor sum of 76,030,220, so this integer is abundant. The Collatz stopping time is 256 steps.

Prime Factor Structure

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

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 130,032,000
Proper Divisor Sum 76,030,220
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #54001763 ← → #54001789

Radix Representation

Decimal 54001780
Binary 11001110000000000001110100 (26 bits)
Octal 0o316000164
Hexadecimal 0x3380074

Divisor Catalog (48)

1 2 4 5 7 10 14 20 28 35 70 140 499 773 998 1,546 1,996 2,495 3,092 3,493 3,865 4,990 5,411 6,986 7,730 9,980 10,822 13,972 15,460 17,465 21,644 27,055 34,930 54,110 69,860 108,220 385,727 771,454 1,542,908 1,928,635 2,700,089 3,857,270 5,400,178 7,714,540 10,800,356 13,500,445 27,000,890 54,001,780

Collatz Trajectory (256 steps to reach 1)

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

54,001,780 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

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