λ
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807,680

28 × 5 × 631
Abundant Even Composite

807,680 factors as 2^8 × 5 × 631. Its 36 positive divisors give a proper-divisor sum of 1,130,032, so this integer is abundant. The Collatz stopping time is 100 steps.

Prime Factor Structure

Factorization String 2^8 × 5 × 631
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 1,937,712
Proper Divisor Sum 1,130,032
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #807647 ← → #807689

Radix Representation

Decimal 807680
Binary 11000101001100000000 (20 bits)
Octal 0o3051400
Hexadecimal 0xC5300

Divisor Catalog (36)

1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 631 640 1,262 1,280 2,524 3,155 5,048 6,310 10,096 12,620 20,192 25,240 40,384 50,480 80,768 100,960 161,536 201,920 403,840 807,680

Collatz Trajectory (100 steps to reach 1)

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

807,680 403,840 201,920 100,960 50,480 25,240 12,620 6,310 3,155 9,466 4,733 14,200 7,100 3,550 1,775 5,326 2,663 7,990 3,995 11,986 5,993 17,980 8,990 4,495 13,486 6,743 20,230 10,115 30,346 15,173 45,520 22,760 11,380 5,690 2,845 8,536 4,268 2,134 1,067 3,202 1,601 4,804 2,402 1,201 3,604 1,802 901 2,704 1,352 676 338 169 508 254 127 382 191 574 287 862

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