217,210

2 × 5 × 7 × 29 × 107

217,210 factors as 2 × 5 × 7 × 29 × 107. Its 32 positive divisors give a proper-divisor sum of 249,350, so this integer is abundant. The Collatz stopping time is 93 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 29 × 107

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 466,560

Proper Divisor Sum 249,350

Digit Sum / Digital Root 13 (Root: 4)

Adjacent Primes #217207 ← → #217219

Radix Representation

Decimal	217210
Binary	110101000001111010 (18 bits)
Octal	0o650172
Hexadecimal	0x3507A

Divisor Catalog (32)

1 2 5 7 10 14 29 35 58 70 107 145 203 214 290 406 535 749 1,015 1,070 1,498 2,030 3,103 3,745 6,206 7,490 15,515 21,721 31,030 43,442 108,605 217,210

Collatz Trajectory (93 steps to reach 1)

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

217,210 108,605 325,816 162,908 81,454 40,727 122,182 61,091 183,274 91,637 274,912 137,456 68,728 34,364 17,182 8,591 25,774 12,887 38,662 19,331 57,994 28,997 86,992 43,496 21,748 10,874 5,437 16,312 8,156 4,078 2,039 6,118 3,059 9,178 4,589 13,768 6,884 3,442 1,721 5,164 2,582 1,291 3,874 1,937 5,812 2,906 1,453 4,360 2,180 1,090 545 1,636 818 409 1,228 614 307 922 461 1,384

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