λ
Harmonic Matrix

480,830

2 × 5 × 7 × 6869
Abundant Even Composite

480,830 has digital root 5. The neighboring primes are 480827 and 480839; its proper-divisor sum differs from the starting integer by 27,620.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 6869
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 989,280
Proper Divisor Sum 508,450
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #480827 ← → #480839

Radix Representation

Decimal 480830
Binary 1110101011000111110 (19 bits)
Octal 0o1653076
Hexadecimal 0x7563E

Divisor Catalog (16)

1 2 5 7 10 14 35 70 6,869 13,738 34,345 48,083 68,690 96,166 240,415 480,830

Collatz Trajectory (94 steps to reach 1)

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

480,830 240,415 721,246 360,623 1,081,870 540,935 1,622,806 811,403 2,434,210 1,217,105 3,651,316 1,825,658 912,829 2,738,488 1,369,244 684,622 342,311 1,026,934 513,467 1,540,402 770,201 2,310,604 1,155,302 577,651 1,732,954 866,477 2,599,432 1,299,716 649,858 324,929 974,788 487,394 243,697 731,092 365,546 182,773 548,320 274,160 137,080 68,540 34,270 17,135 51,406 25,703 77,110 38,555 115,666 57,833 173,500 86,750 43,375 130,126 65,063 195,190 97,595 292,786 146,393 439,180 219,590 109,795

More profiles

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