91,188

2² × 3² × 17 × 149

Starting at 91,188, the Collatz iteration reaches 1 after 71 steps. The first transition is 45594; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 17 × 149

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 245,700

Proper Divisor Sum 154,512

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #91183 ← → #91193

Radix Representation

Decimal	91188
Binary	10110010000110100 (17 bits)
Octal	0o262064
Hexadecimal	0x16434

Divisor Catalog (36)

1 2 3 4 6 9 12 17 18 34 36 51 68 102 149 153 204 298 306 447 596 612 894 1,341 1,788 2,533 2,682 5,066 5,364 7,599 10,132 15,198 22,797 30,396 45,594 91,188

Collatz Trajectory (71 steps to reach 1)

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

91,188 45,594 22,797 68,392 34,196 17,098 8,549 25,648 12,824 6,412 3,206 1,603 4,810 2,405 7,216 3,608 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382 191 574 287 862 431 1,294 647 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17

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