467,280

2⁴ × 3² × 5 × 11 × 59

For 467,280, the 120 positive divisors have a total of 1,740,960. Removing 467,280 leaves 1,273,680, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 5 × 11 × 59

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 1,740,960

Proper Divisor Sum 1,273,680

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #467261 ← → #467293

Radix Representation

Decimal	467280
Binary	1110010000101010000 (19 bits)
Octal	0o1620520
Hexadecimal	0x72150

Divisor Catalog (60 of 120)

1 2 3 4 5 6 8 9 10 11 12 15 16 18 20 22 24 30 33 36 40 44 45 48 55 59 60 66 72 80 88 90 99 110 118 120 132 144 165 176 177 180 198 220 236 240 264 295 330 354 360 396 440 472 495 528 531 590 649 660

Collatz Trajectory (50 steps to reach 1)

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

467,280 233,640 116,820 58,410 29,205 87,616 43,808 21,904 10,952 5,476 2,738 1,369 4,108 2,054 1,027 3,082 1,541 4,624 2,312 1,156 578 289 868 434 217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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