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828,090

2 × 33 × 5 × 3067
Abundant Even Composite

828,090 factors as 2 × 3^3 × 5 × 3067. Its 32 positive divisors give a proper-divisor sum of 1,380,870, so this integer is abundant. The Collatz stopping time is 175 steps.

Prime Factor Structure

Factorization String 2 × 3^3 × 5 × 3067
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 2,208,960
Proper Divisor Sum 1,380,870
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #828071 ← → #828101

Radix Representation

Decimal 828090
Binary 11001010001010111010 (20 bits)
Octal 0o3121272
Hexadecimal 0xCA2BA

Divisor Catalog (32)

1 2 3 5 6 9 10 15 18 27 30 45 54 90 135 270 3,067 6,134 9,201 15,335 18,402 27,603 30,670 46,005 55,206 82,809 92,010 138,015 165,618 276,030 414,045 828,090

Collatz Trajectory (175 steps to reach 1)

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

828,090 414,045 1,242,136 621,068 310,534 155,267 465,802 232,901 698,704 349,352 174,676 87,338 43,669 131,008 65,504 32,752 16,376 8,188 4,094 2,047 6,142 3,071 9,214 4,607 13,822 6,911 20,734 10,367 31,102 15,551 46,654 23,327 69,982 34,991 104,974 52,487 157,462 78,731 236,194 118,097 354,292 177,146 88,573 265,720 132,860 66,430 33,215 99,646 49,823 149,470 74,735 224,206 112,103 336,310 168,155 504,466 252,233 756,700 378,350 189,175

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