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Atlas › Integer Profiles › Node 26,318,100

26,318,100

22 × 3 × 52 × 37 × 2371
Abundant Even Composite

26,318,100 factors as 2^2 × 3 × 5^2 × 37 × 2371. Its 72 positive divisors give a proper-divisor sum of 51,919,948, so this integer is abundant. The Collatz stopping time is 211 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^2 × 37 × 2371
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 78,238,048
Proper Divisor Sum 51,919,948
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #26318099 ← → #26318129

Radix Representation

Decimal 26318100
Binary 1100100011001010100010100 (25 bits)
Octal 0o144312424
Hexadecimal 0x1919514

Divisor Catalog (60 of 72)

1 2 3 4 5 6 10 12 15 20 25 30 37 50 60 74 75 100 111 148 150 185 222 300 370 444 555 740 925 1,110 1,850 2,220 2,371 2,775 3,700 4,742 5,550 7,113 9,484 11,100 11,855 14,226 23,710 28,452 35,565 47,420 59,275 71,130 87,727 118,550 142,260 175,454 177,825 237,100 263,181 350,908 355,650 438,635 526,362 711,300

Collatz Trajectory (211 steps to reach 1)

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

26,318,100 13,159,050 6,579,525 19,738,576 9,869,288 4,934,644 2,467,322 1,233,661 3,700,984 1,850,492 925,246 462,623 1,387,870 693,935 2,081,806 1,040,903 3,122,710 1,561,355 4,684,066 2,342,033 7,026,100 3,513,050 1,756,525 5,269,576 2,634,788 1,317,394 658,697 1,976,092 988,046 494,023 1,482,070 741,035 2,223,106 1,111,553 3,334,660 1,667,330 833,665 2,500,996 1,250,498 625,249 1,875,748 937,874 468,937 1,406,812 703,406 351,703 1,055,110 527,555 1,582,666 791,333 2,374,000 1,187,000 593,500 296,750 148,375 445,126 222,563 667,690 333,845 1,001,536

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