64,512

2¹⁰ × 3² × 7

64,512 factors as 2^10 × 3^2 × 7. Its 66 positive divisors give a proper-divisor sum of 148,376, so this integer is abundant. The Collatz stopping time is 117 steps.

Prime Factor Structure

Factorization String 2^10 × 3^2 × 7

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 66

Divisor Sum (σ) 212,888

Proper Divisor Sum 148,376

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #64499 ← → #64513

Radix Representation

Decimal	64512
Binary	1111110000000000 (16 bits)
Octal	0o176000
Hexadecimal	0xFC00

Divisor Catalog (60 of 66)

1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 32 36 42 48 56 63 64 72 84 96 112 126 128 144 168 192 224 252 256 288 336 384 448 504 512 576 672 768 896 1,008 1,024 1,152 1,344 1,536 1,792 2,016 2,304 2,688 3,072 3,584 4,032 4,608 5,376 7,168 8,064

Collatz Trajectory (117 steps to reach 1)

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

64,512 32,256 16,128 8,064 4,032 2,016 1,008 504 252 126 63 190 95 286 143 430 215 646 323 970 485 1,456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425

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