156,288

2⁷ × 3 × 11 × 37

156,288 factors as 2^7 × 3 × 11 × 37. Its 64 positive divisors give a proper-divisor sum of 308,832, so this integer is abundant. The Collatz stopping time is 46 steps.

Prime Factor Structure

Factorization String 2^7 × 3 × 11 × 37

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 465,120

Proper Divisor Sum 308,832

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #156269 ← → #156307

Radix Representation

Decimal	156288
Binary	100110001010000000 (18 bits)
Octal	0o461200
Hexadecimal	0x26280

Divisor Catalog (60 of 64)

1 2 3 4 6 8 11 12 16 22 24 32 33 37 44 48 64 66 74 88 96 111 128 132 148 176 192 222 264 296 352 384 407 444 528 592 704 814 888 1,056 1,184 1,221 1,408 1,628 1,776 2,112 2,368 2,442 3,256 3,552 4,224 4,736 4,884 6,512 7,104 9,768 13,024 14,208 19,536 26,048

Collatz Trajectory (46 steps to reach 1)

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

156,288 78,144 39,072 19,536 9,768 4,884 2,442 1,221 3,664 1,832 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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