194,184

2³ × 3³ × 29 × 31

194,184 factors as 2^3 × 3^3 × 29 × 31. Its 64 positive divisors give a proper-divisor sum of 381,816, so this integer is abundant. The Collatz stopping time is 191 steps.

Prime Factor Structure

Factorization String 2^3 × 3^3 × 29 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 576,000

Proper Divisor Sum 381,816

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #194179 ← → #194197

Radix Representation

Decimal	194184
Binary	101111011010001000 (18 bits)
Octal	0o573210
Hexadecimal	0x2F688

Divisor Catalog (60 of 64)

1 2 3 4 6 8 9 12 18 24 27 29 31 36 54 58 62 72 87 93 108 116 124 174 186 216 232 248 261 279 348 372 522 558 696 744 783 837 899 1,044 1,116 1,566 1,674 1,798 2,088 2,232 2,697 3,132 3,348 3,596 5,394 6,264 6,696 7,192 8,091 10,788 16,182 21,576 24,273 32,364

Collatz Trajectory (191 steps to reach 1)

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

194,184 97,092 48,546 24,273 72,820 36,410 18,205 54,616 27,308 13,654 6,827 20,482 10,241 30,724 15,362 7,681 23,044 11,522 5,761 17,284 8,642 4,321 12,964 6,482 3,241 9,724 4,862 2,431 7,294 3,647 10,942 5,471 16,414 8,207 24,622 12,311 36,934 18,467 55,402 27,701 83,104 41,552 20,776 10,388 5,194 2,597 7,792 3,896 1,948 974 487 1,462 731 2,194 1,097 3,292 1,646 823 2,470 1,235

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