217,500

2² × 3 × 5⁴ × 29

217,500 has the prime decomposition 2^2 × 3 × 5^4 × 29. Its 4 distinct prime factors produce 60 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^4 × 29

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 656,040

Proper Divisor Sum 438,540

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #217499 ← → #217517

Radix Representation

Decimal	217500
Binary	110101000110011100 (18 bits)
Octal	0o650634
Hexadecimal	0x3519C

Divisor Catalog (60)

1 2 3 4 5 6 10 12 15 20 25 29 30 50 58 60 75 87 100 116 125 145 150 174 250 290 300 348 375 435 500 580 625 725 750 870 1,250 1,450 1,500 1,740 1,875 2,175 2,500 2,900 3,625 3,750 4,350 7,250 7,500 8,700 10,875 14,500 18,125 21,750 36,250 43,500 54,375 72,500 108,750 217,500

Collatz Trajectory (142 steps to reach 1)

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

217,500 108,750 54,375 163,126 81,563 244,690 122,345 367,036 183,518 91,759 275,278 137,639 412,918 206,459 619,378 309,689 929,068 464,534 232,267 696,802 348,401 1,045,204 522,602 261,301 783,904 391,952 195,976 97,988 48,994 24,497 73,492 36,746 18,373 55,120 27,560 13,780 6,890 3,445 10,336 5,168 2,584 1,292 646 323 970 485 1,456 728 364 182 91 274 137 412 206 103 310 155 466 233

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