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Atlas › Integer Profiles › Node 32,640,520

32,640,520

23 × 5 × 11 × 31 × 2393
Abundant Even Composite

32,640,520 factors as 2^3 × 5 × 11 × 31 × 2393. Its 64 positive divisors give a proper-divisor sum of 50,096,120, so this integer is abundant. The Collatz stopping time is 201 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 11 × 31 × 2393
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 82,736,640
Proper Divisor Sum 50,096,120
Digit Sum / Digital Root 22 (Root: 4)
Adjacent Primes #32640481 ← → #32640529

Radix Representation

Decimal 32640520
Binary 1111100100000111000001000 (25 bits)
Octal 0o174407010
Hexadecimal 0x1F20E08

Divisor Catalog (60 of 64)

1 2 4 5 8 10 11 20 22 31 40 44 55 62 88 110 124 155 220 248 310 341 440 620 682 1,240 1,364 1,705 2,393 2,728 3,410 4,786 6,820 9,572 11,965 13,640 19,144 23,930 26,323 47,860 52,646 74,183 95,720 105,292 131,615 148,366 210,584 263,230 296,732 370,915 526,460 593,464 741,830 816,013 1,052,920 1,483,660 1,632,026 2,967,320 3,264,052 4,080,065

Collatz Trajectory (201 steps to reach 1)

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

32,640,520 16,320,260 8,160,130 4,080,065 12,240,196 6,120,098 3,060,049 9,180,148 4,590,074 2,295,037 6,885,112 3,442,556 1,721,278 860,639 2,581,918 1,290,959 3,872,878 1,936,439 5,809,318 2,904,659 8,713,978 4,356,989 13,070,968 6,535,484 3,267,742 1,633,871 4,901,614 2,450,807 7,352,422 3,676,211 11,028,634 5,514,317 16,542,952 8,271,476 4,135,738 2,067,869 6,203,608 3,101,804 1,550,902 775,451 2,326,354 1,163,177 3,489,532 1,744,766 872,383 2,617,150 1,308,575 3,925,726 1,962,863 5,888,590 2,944,295 8,832,886 4,416,443 13,249,330 6,624,665 19,873,996 9,936,998 4,968,499 14,905,498 7,452,749

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