37,734

2 × 3 × 19 × 331

37,734 factors as 2 × 3 × 19 × 331. Its 16 positive divisors give a proper-divisor sum of 41,946, so this integer is abundant. The Collatz stopping time is 36 steps.

Prime Factor Structure

Factorization String 2 × 3 × 19 × 331

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 79,680

Proper Divisor Sum 41,946

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #37717 ← → #37747

Radix Representation

Decimal	37734
Binary	1001001101100110 (16 bits)
Octal	0o111546
Hexadecimal	0x9366

Divisor Catalog (16)

1 2 3 6 19 38 57 114 331 662 993 1,986 6,289 12,578 18,867 37,734

Collatz Trajectory (36 steps to reach 1)

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

37,734 18,867 56,602 28,301 84,904 42,452 21,226 10,613 31,840 15,920 7,960 3,980 1,990 995 2,986 1,493 4,480 2,240 1,120 560 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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