216,384

2⁶ × 3 × 7² × 23

For 216,384, the 84 positive divisors have a total of 694,944. Removing 216,384 leaves 478,560, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^6 × 3 × 7^2 × 23

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 84

Divisor Sum (σ) 694,944

Proper Divisor Sum 478,560

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #216379 ← → #216397

Radix Representation

Decimal	216384
Binary	110100110101000000 (18 bits)
Octal	0o646500
Hexadecimal	0x34D40

Divisor Catalog (60 of 84)

1 2 3 4 6 7 8 12 14 16 21 23 24 28 32 42 46 48 49 56 64 69 84 92 96 98 112 138 147 161 168 184 192 196 224 276 294 322 336 368 392 448 483 552 588 644 672 736 784 966 1,104 1,127 1,176 1,288 1,344 1,472 1,568 1,932 2,208 2,254

Collatz Trajectory (49 steps to reach 1)

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

216,384 108,192 54,096 27,048 13,524 6,762 3,381 10,144 5,072 2,536 1,268 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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