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6,480,090

2 × 32 × 5 × 89 × 809
Abundant Even Composite

6,480,090 factors as 2 × 3^2 × 5 × 89 × 809. Its 48 positive divisors give a proper-divisor sum of 10,578,510, so this integer is abundant. The Collatz stopping time is 90 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 89 × 809
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 17,058,600
Proper Divisor Sum 10,578,510
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #6480053 ← → #6480107

Radix Representation

Decimal 6480090
Binary 11000101110000011011010 (23 bits)
Octal 0o30560332
Hexadecimal 0x62E0DA

Divisor Catalog (48)

1 2 3 5 6 9 10 15 18 30 45 89 90 178 267 445 534 801 809 890 1,335 1,602 1,618 2,427 2,670 4,005 4,045 4,854 7,281 8,010 8,090 12,135 14,562 24,270 36,405 72,001 72,810 144,002 216,003 360,005 432,006 648,009 720,010 1,080,015 1,296,018 2,160,030 3,240,045 6,480,090

Collatz Trajectory (90 steps to reach 1)

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

6,480,090 3,240,045 9,720,136 4,860,068 2,430,034 1,215,017 3,645,052 1,822,526 911,263 2,733,790 1,366,895 4,100,686 2,050,343 6,151,030 3,075,515 9,226,546 4,613,273 13,839,820 6,919,910 3,459,955 10,379,866 5,189,933 15,569,800 7,784,900 3,892,450 1,946,225 5,838,676 2,919,338 1,459,669 4,379,008 2,189,504 1,094,752 547,376 273,688 136,844 68,422 34,211 102,634 51,317 153,952 76,976 38,488 19,244 9,622 4,811 14,434 7,217 21,652 10,826 5,413 16,240 8,120 4,060 2,030 1,015 3,046 1,523 4,570 2,285 6,856

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