λ
Harmonic Matrix

680,796

22 × 32 × 18911
Abundant Even Composite

680,796 has digital root 9. The neighboring primes are 680783 and 680803; its proper-divisor sum differs from the starting integer by 359,400.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 18911
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 18
Divisor Sum (σ) 1,720,992
Proper Divisor Sum 1,040,196
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #680783 ← → #680803

Radix Representation

Decimal 680796
Binary 10100110001101011100 (20 bits)
Octal 0o2461534
Hexadecimal 0xA635C

Divisor Catalog (18)

1 2 3 4 6 9 12 18 36 18,911 37,822 56,733 75,644 113,466 170,199 226,932 340,398 680,796

Collatz Trajectory (66 steps to reach 1)

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

680,796 340,398 170,199 510,598 255,299 765,898 382,949 1,148,848 574,424 287,212 143,606 71,803 215,410 107,705 323,116 161,558 80,779 242,338 121,169 363,508 181,754 90,877 272,632 136,316 68,158 34,079 102,238 51,119 153,358 76,679 230,038 115,019 345,058 172,529 517,588 258,794 129,397 388,192 194,096 97,048 48,524 24,262 12,131 36,394 18,197 54,592 27,296 13,648 6,824 3,412 1,706 853 2,560 1,280 640 320 160 80 40 20

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