8,082,288

2⁴ × 3³ × 53 × 353

8,082,288 factors as 2^4 × 3^3 × 53 × 353. Its 80 positive divisors give a proper-divisor sum of 15,621,552, so this integer is abundant. The Collatz stopping time is 186 steps.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 53 × 353

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 23,703,840

Proper Divisor Sum 15,621,552

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8082287 ← → #8082301

Radix Representation

Decimal	8082288
Binary	11110110101001101110000 (23 bits)
Octal	0o36651560
Hexadecimal	0x7B5370

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 12 16 18 24 27 36 48 53 54 72 106 108 144 159 212 216 318 353 424 432 477 636 706 848 954 1,059 1,272 1,412 1,431 1,908 2,118 2,544 2,824 2,862 3,177 3,816 4,236 5,648 5,724 6,354 7,632 8,472 9,531 11,448 12,708 16,944 18,709 19,062 22,896 25,416 37,418 38,124 50,832

Collatz Trajectory (186 steps to reach 1)

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

8,082,288 4,041,144 2,020,572 1,010,286 505,143 1,515,430 757,715 2,273,146 1,136,573 3,409,720 1,704,860 852,430 426,215 1,278,646 639,323 1,917,970 958,985 2,876,956 1,438,478 719,239 2,157,718 1,078,859 3,236,578 1,618,289 4,854,868 2,427,434 1,213,717 3,641,152 1,820,576 910,288 455,144 227,572 113,786 56,893 170,680 85,340 42,670 21,335 64,006 32,003 96,010 48,005 144,016 72,008 36,004 18,002 9,001 27,004 13,502 6,751 20,254 10,127 30,382 15,191 45,574 22,787 68,362 34,181 102,544 51,272

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