33,444

2² × 3² × 929

Starting at 33,444, the Collatz iteration reaches 1 after 116 steps. The first transition is 16722; the starting value is even with 18 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 929

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 18

Divisor Sum (σ) 84,630

Proper Divisor Sum 51,186

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #33427 ← → #33457

Radix Representation

Decimal	33444
Binary	1000001010100100 (16 bits)
Octal	0o101244
Hexadecimal	0x82A4

Divisor Catalog (18)

1 2 3 4 6 9 12 18 36 929 1,858 2,787 3,716 5,574 8,361 11,148 16,722 33,444

Collatz Trajectory (116 steps to reach 1)

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

33,444 16,722 8,361 25,084 12,542 6,271 18,814 9,407 28,222 14,111 42,334 21,167 63,502 31,751 95,254 47,627 142,882 71,441 214,324 107,162 53,581 160,744 80,372 40,186 20,093 60,280 30,140 15,070 7,535 22,606 11,303 33,910 16,955 50,866 25,433 76,300 38,150 19,075 57,226 28,613 85,840 42,920 21,460 10,730 5,365 16,096 8,048 4,024 2,012 1,006 503 1,510 755 2,266 1,133 3,400 1,700 850 425 1,276

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