73,728

2¹³ × 3²

73,728 is even and not a perfect square. Its factorization is 2^13 × 3^2 and its 42 divisors sum to 212,979.

Prime Factor Structure

Factorization String 2^13 × 3^2

Distinct Prime Factors 2

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 42

Divisor Sum (σ) 212,979

Proper Divisor Sum 139,251

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #73727 ← → #73751

Radix Representation

Decimal	73728
Binary	10010000000000000 (17 bits)
Octal	0o220000
Hexadecimal	0x12000

Divisor Catalog (42)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 128 144 192 256 288 384 512 576 768 1,024 1,152 1,536 2,048 2,304 3,072 4,096 4,608 6,144 8,192 9,216 12,288 18,432 24,576 36,864 73,728

Collatz Trajectory (32 steps to reach 1)

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

73,728 36,864 18,432 9,216 4,608 2,304 1,152 576 288 144 72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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