409,488

2⁴ × 3 × 19 × 449

409,488 has the prime decomposition 2^4 × 3 × 19 × 449. Its 4 distinct prime factors produce 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 19 × 449

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 1,116,000

Proper Divisor Sum 706,512

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #409483 ← → #409499

Radix Representation

Decimal	409488
Binary	1100011111110010000 (19 bits)
Octal	0o1437620
Hexadecimal	0x63F90

Divisor Catalog (40)

1 2 3 4 6 8 12 16 19 24 38 48 57 76 114 152 228 304 449 456 898 912 1,347 1,796 2,694 3,592 5,388 7,184 8,531 10,776 17,062 21,552 25,593 34,124 51,186 68,248 102,372 136,496 204,744 409,488

Collatz Trajectory (205 steps to reach 1)

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

409,488 204,744 102,372 51,186 25,593 76,780 38,390 19,195 57,586 28,793 86,380 43,190 21,595 64,786 32,393 97,180 48,590 24,295 72,886 36,443 109,330 54,665 163,996 81,998 40,999 122,998 61,499 184,498 92,249 276,748 138,374 69,187 207,562 103,781 311,344 155,672 77,836 38,918 19,459 58,378 29,189 87,568 43,784 21,892 10,946 5,473 16,420 8,210 4,105 12,316 6,158 3,079 9,238 4,619 13,858 6,929 20,788 10,394 5,197 15,592

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