λ
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Atlas › Integer Profiles › Node 36,927,288

36,927,288

23 × 32 × 401 × 1279
Abundant Even Composite

36,927,288 factors as 2^3 × 3^2 × 401 × 1279. Its 48 positive divisors give a proper-divisor sum of 63,411,912, so this integer is abundant. The Collatz stopping time is 188 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 401 × 1279
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 100,339,200
Proper Divisor Sum 63,411,912
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #36927287 ← → #36927301

Radix Representation

Decimal 36927288
Binary 10001100110111011100111000 (26 bits)
Octal 0o214673470
Hexadecimal 0x2337738

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 72 401 802 1,203 1,279 1,604 2,406 2,558 3,208 3,609 3,837 4,812 5,116 7,218 7,674 9,624 10,232 11,511 14,436 15,348 23,022 28,872 30,696 46,044 92,088 512,879 1,025,758 1,538,637 2,051,516 3,077,274 4,103,032 4,615,911 6,154,548 9,231,822 12,309,096 18,463,644 36,927,288

Collatz Trajectory (188 steps to reach 1)

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

36,927,288 18,463,644 9,231,822 4,615,911 13,847,734 6,923,867 20,771,602 10,385,801 31,157,404 15,578,702 7,789,351 23,368,054 11,684,027 35,052,082 17,526,041 52,578,124 26,289,062 13,144,531 39,433,594 19,716,797 59,150,392 29,575,196 14,787,598 7,393,799 22,181,398 11,090,699 33,272,098 16,636,049 49,908,148 24,954,074 12,477,037 37,431,112 18,715,556 9,357,778 4,678,889 14,036,668 7,018,334 3,509,167 10,527,502 5,263,751 15,791,254 7,895,627 23,686,882 11,843,441 35,530,324 17,765,162 8,882,581 26,647,744 13,323,872 6,661,936 3,330,968 1,665,484 832,742 416,371 1,249,114 624,557 1,873,672 936,836 468,418 234,209

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