21,330

2 × 3³ × 5 × 79

Starting at 21,330, the Collatz iteration reaches 1 after 193 steps. The first transition is 10665; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^3 × 5 × 79

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 57,600

Proper Divisor Sum 36,270

Digit Sum / Digital Root 9 (Root: 9)

Adjacent Primes #21323 ← → #21341

Radix Representation

Decimal	21330
Binary	101001101010010 (15 bits)
Octal	0o51522
Hexadecimal	0x5352

Divisor Catalog (32)

1 2 3 5 6 9 10 15 18 27 30 45 54 79 90 135 158 237 270 395 474 711 790 1,185 1,422 2,133 2,370 3,555 4,266 7,110 10,665 21,330

Collatz Trajectory (193 steps to reach 1)

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

21,330 10,665 31,996 15,998 7,999 23,998 11,999 35,998 17,999 53,998 26,999 80,998 40,499 121,498 60,749 182,248 91,124 45,562 22,781 68,344 34,172 17,086 8,543 25,630 12,815 38,446 19,223 57,670 28,835 86,506 43,253 129,760 64,880 32,440 16,220 8,110 4,055 12,166 6,083 18,250 9,125 27,376 13,688 6,844 3,422 1,711 5,134 2,567 7,702 3,851 11,554 5,777 17,332 8,666 4,333 13,000 6,500 3,250 1,625 4,876

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