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Atlas › Integer Profiles › Node 45,189,270

45,189,270

2 × 32 × 5 × 72 × 10247
Abundant Even Composite

45,189,270 factors as 2 × 3^2 × 5 × 7^2 × 10247. Its 72 positive divisors give a proper-divisor sum of 91,498,554, so this integer is abundant. The Collatz stopping time is 129 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 7^2 × 10247
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 136,687,824
Proper Divisor Sum 91,498,554
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #45189253 ← → #45189271

Radix Representation

Decimal 45189270
Binary 10101100011000100010010110 (26 bits)
Octal 0o254304226
Hexadecimal 0x2B18896

Divisor Catalog (60 of 72)

1 2 3 5 6 7 9 10 14 15 18 21 30 35 42 45 49 63 70 90 98 105 126 147 210 245 294 315 441 490 630 735 882 1,470 2,205 4,410 10,247 20,494 30,741 51,235 61,482 71,729 92,223 102,470 143,458 153,705 184,446 215,187 307,410 358,645 430,374 461,115 502,103 645,561 717,290 922,230 1,004,206 1,075,935 1,291,122 1,506,309

Collatz Trajectory (129 steps to reach 1)

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

45,189,270 22,594,635 67,783,906 33,891,953 101,675,860 50,837,930 25,418,965 76,256,896 38,128,448 19,064,224 9,532,112 4,766,056 2,383,028 1,191,514 595,757 1,787,272 893,636 446,818 223,409 670,228 335,114 167,557 502,672 251,336 125,668 62,834 31,417 94,252 47,126 23,563 70,690 35,345 106,036 53,018 26,509 79,528 39,764 19,882 9,941 29,824 14,912 7,456 3,728 1,864 932 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336

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