λ
Prime Ledger

727,684

22 × 109 × 1669
Deficient Even Composite

727,684 has the prime decomposition 2^2 × 109 × 1669. Its 3 distinct prime factors produce 12 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 109 × 1669
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 1,285,900
Proper Divisor Sum 558,216
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #727673 ← → #727691

Radix Representation

Decimal 727684
Binary 10110001101010000100 (20 bits)
Octal 0o2615204
Hexadecimal 0xB1A84

Divisor Catalog (12)

1 2 4 109 218 436 1,669 3,338 6,676 181,921 363,842 727,684

Collatz Trajectory (180 steps to reach 1)

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

727,684 363,842 181,921 545,764 272,882 136,441 409,324 204,662 102,331 306,994 153,497 460,492 230,246 115,123 345,370 172,685 518,056 259,028 129,514 64,757 194,272 97,136 48,568 24,284 12,142 6,071 18,214 9,107 27,322 13,661 40,984 20,492 10,246 5,123 15,370 7,685 23,056 11,528 5,764 2,882 1,441 4,324 2,162 1,081 3,244 1,622 811 2,434 1,217 3,652 1,826 913 2,740 1,370 685 2,056 1,028 514 257 772

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