728,004

2² × 3 × 19 × 31 × 103

728,004 has digital root 3. The neighboring primes are 728003 and 728017; its proper-divisor sum differs from the starting integer by 407,672.

Prime Factor Structure

Factorization String 2^2 × 3 × 19 × 31 × 103

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,863,680

Proper Divisor Sum 1,135,676

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #728003 ← → #728017

Radix Representation

Decimal	728004
Binary	10110001101111000100 (20 bits)
Octal	0o2615704
Hexadecimal	0xB1BC4

Divisor Catalog (48)

1 2 3 4 6 12 19 31 38 57 62 76 93 103 114 124 186 206 228 309 372 412 589 618 1,178 1,236 1,767 1,957 2,356 3,193 3,534 3,914 5,871 6,386 7,068 7,828 9,579 11,742 12,772 19,158 23,484 38,316 60,667 121,334 182,001 242,668 364,002 728,004

Collatz Trajectory (180 steps to reach 1)

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

728,004 364,002 182,001 546,004 273,002 136,501 409,504 204,752 102,376 51,188 25,594 12,797 38,392 19,196 9,598 4,799 14,398 7,199 21,598 10,799 32,398 16,199 48,598 24,299 72,898 36,449 109,348 54,674 27,337 82,012 41,006 20,503 61,510 30,755 92,266 46,133 138,400 69,200 34,600 17,300 8,650 4,325 12,976 6,488 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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