59,328

2⁶ × 3² × 103

59,328 factors as 2^6 × 3^2 × 103. Its 42 positive divisors give a proper-divisor sum of 112,376, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^6 × 3^2 × 103

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 42

Divisor Sum (σ) 171,704

Proper Divisor Sum 112,376

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #59281 ← → #59333

Radix Representation

Decimal	59328
Binary	1110011111000000 (16 bits)
Octal	0o163700
Hexadecimal	0xE7C0

Divisor Catalog (42)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 103 144 192 206 288 309 412 576 618 824 927 1,236 1,648 1,854 2,472 3,296 3,708 4,944 6,592 7,416 9,888 14,832 19,776 29,664 59,328

Collatz Trajectory (122 steps to reach 1)

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

59,328 29,664 14,832 7,416 3,708 1,854 927 2,782 1,391 4,174 2,087 6,262 3,131 9,394 4,697 14,092 7,046 3,523 10,570 5,285 15,856 7,928 3,964 1,982 991 2,974 1,487 4,462 2,231 6,694 3,347 10,042 5,021 15,064 7,532 3,766 1,883 5,650 2,825 8,476 4,238 2,119 6,358 3,179 9,538 4,769 14,308 7,154 3,577 10,732 5,366 2,683 8,050 4,025 12,076 6,038 3,019 9,058 4,529 13,588

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