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77,666,300

22 × 52 × 19 × 41 × 997
Abundant Even Composite

77,666,300 factors as 2^2 × 5^2 × 19 × 41 × 997. Its 72 positive divisors give a proper-divisor sum of 104,249,140, so this integer is abundant. The Collatz stopping time is 254 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 19 × 41 × 997
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 181,915,440
Proper Divisor Sum 104,249,140
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #77666297 ← → #77666339

Radix Representation

Decimal 77666300
Binary 100101000010001011111111100 (27 bits)
Octal 0o450213774
Hexadecimal 0x4A117FC

Divisor Catalog (60 of 72)

1 2 4 5 10 19 20 25 38 41 50 76 82 95 100 164 190 205 380 410 475 779 820 950 997 1,025 1,558 1,900 1,994 2,050 3,116 3,895 3,988 4,100 4,985 7,790 9,970 15,580 18,943 19,475 19,940 24,925 37,886 38,950 40,877 49,850 75,772 77,900 81,754 94,715 99,700 163,508 189,430 204,385 378,860 408,770 473,575 776,663 817,540 947,150

Collatz Trajectory (254 steps to reach 1)

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

77,666,300 38,833,150 19,416,575 58,249,726 29,124,863 87,374,590 43,687,295 131,061,886 65,530,943 196,592,830 98,296,415 294,889,246 147,444,623 442,333,870 221,166,935 663,500,806 331,750,403 995,251,210 497,625,605 1,492,876,816 746,438,408 373,219,204 186,609,602 93,304,801 279,914,404 139,957,202 69,978,601 209,935,804 104,967,902 52,483,951 157,451,854 78,725,927 236,177,782 118,088,891 354,266,674 177,133,337 531,400,012 265,700,006 132,850,003 398,550,010 199,275,005 597,825,016 298,912,508 149,456,254 74,728,127 224,184,382 112,092,191 336,276,574 168,138,287 504,414,862 252,207,431 756,622,294 378,311,147 1,134,933,442 567,466,721 1,702,400,164 851,200,082 425,600,041 1,276,800,124 638,400,062

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