38,208

2⁶ × 3 × 199

38,208 factors as 2^6 × 3 × 199. Its 28 positive divisors give a proper-divisor sum of 63,392, so this integer is abundant. The Collatz stopping time is 31 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 199

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 28

Divisor Sum (σ) 101,600

Proper Divisor Sum 63,392

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #38201 ← → #38219

Radix Representation

Decimal	38208
Binary	1001010101000000 (16 bits)
Octal	0o112500
Hexadecimal	0x9540

Divisor Catalog (28)

1 2 3 4 6 8 12 16 24 32 48 64 96 192 199 398 597 796 1,194 1,592 2,388 3,184 4,776 6,368 9,552 12,736 19,104 38,208

Collatz Trajectory (31 steps to reach 1)

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

38,208 19,104 9,552 4,776 2,388 1,194 597 1,792 896 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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