λ
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Atlas › Integer Profiles › Node 26,327,928

26,327,928

23 × 3 × 11 × 31 × 3217
Abundant Even Composite

26,327,928 factors as 2^3 × 3 × 11 × 31 × 3217. Its 64 positive divisors give a proper-divisor sum of 47,814,792, so this integer is abundant. The Collatz stopping time is 118 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 11 × 31 × 3217
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 74,142,720
Proper Divisor Sum 47,814,792
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #26327887 ← → #26327929

Radix Representation

Decimal 26327928
Binary 1100100011011101101111000 (25 bits)
Octal 0o144335570
Hexadecimal 0x191BB78

Divisor Catalog (60 of 64)

1 2 3 4 6 8 11 12 22 24 31 33 44 62 66 88 93 124 132 186 248 264 341 372 682 744 1,023 1,364 2,046 2,728 3,217 4,092 6,434 8,184 9,651 12,868 19,302 25,736 35,387 38,604 70,774 77,208 99,727 106,161 141,548 199,454 212,322 283,096 299,181 398,908 424,644 598,362 797,816 849,288 1,096,997 1,196,724 2,193,994 2,393,448 3,290,991 4,387,988

Collatz Trajectory (118 steps to reach 1)

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

26,327,928 13,163,964 6,581,982 3,290,991 9,872,974 4,936,487 14,809,462 7,404,731 22,214,194 11,107,097 33,321,292 16,660,646 8,330,323 24,990,970 12,495,485 37,486,456 18,743,228 9,371,614 4,685,807 14,057,422 7,028,711 21,086,134 10,543,067 31,629,202 15,814,601 47,443,804 23,721,902 11,860,951 35,582,854 17,791,427 53,374,282 26,687,141 80,061,424 40,030,712 20,015,356 10,007,678 5,003,839 15,011,518 7,505,759 22,517,278 11,258,639 33,775,918 16,887,959 50,663,878 25,331,939 75,995,818 37,997,909 113,993,728 56,996,864 28,498,432 14,249,216 7,124,608 3,562,304 1,781,152 890,576 445,288 222,644 111,322 55,661 166,984

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