λ
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Atlas › Integer Profiles › Node 36,734,628

36,734,628

22 × 3 × 7 × 31 × 14107
Abundant Even Composite

36,734,628 factors as 2^2 × 3 × 7 × 31 × 14107. Its 48 positive divisors give a proper-divisor sum of 64,391,516, so this integer is abundant. The Collatz stopping time is 289 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 31 × 14107
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 101,126,144
Proper Divisor Sum 64,391,516
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #36734617 ← → #36734629

Radix Representation

Decimal 36734628
Binary 10001100001000011010100100 (26 bits)
Octal 0o214103244
Hexadecimal 0x23086A4

Divisor Catalog (48)

1 2 3 4 6 7 12 14 21 28 31 42 62 84 93 124 186 217 372 434 651 868 1,302 2,604 14,107 28,214 42,321 56,428 84,642 98,749 169,284 197,498 296,247 394,996 437,317 592,494 874,634 1,184,988 1,311,951 1,749,268 2,623,902 3,061,219 5,247,804 6,122,438 9,183,657 12,244,876 18,367,314 36,734,628

Collatz Trajectory (289 steps to reach 1)

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

36,734,628 18,367,314 9,183,657 27,550,972 13,775,486 6,887,743 20,663,230 10,331,615 30,994,846 15,497,423 46,492,270 23,246,135 69,738,406 34,869,203 104,607,610 52,303,805 156,911,416 78,455,708 39,227,854 19,613,927 58,841,782 29,420,891 88,262,674 44,131,337 132,394,012 66,197,006 33,098,503 99,295,510 49,647,755 148,943,266 74,471,633 223,414,900 111,707,450 55,853,725 167,561,176 83,780,588 41,890,294 20,945,147 62,835,442 31,417,721 94,253,164 47,126,582 23,563,291 70,689,874 35,344,937 106,034,812 53,017,406 26,508,703 79,526,110 39,763,055 119,289,166 59,644,583 178,933,750 89,466,875 268,400,626 134,200,313 402,600,940 201,300,470 100,650,235 301,950,706

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