537,768

2³ × 3² × 7 × 11 × 97

Starting at 537,768, the Collatz iteration reaches 1 after 71 steps. The first transition is 268884; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 7 × 11 × 97

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 1,834,560

Proper Divisor Sum 1,296,792

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #537749 ← → #537769

Radix Representation

Decimal	537768
Binary	10000011010010101000 (20 bits)
Octal	0o2032250
Hexadecimal	0x834A8

Divisor Catalog (60 of 96)

1 2 3 4 6 7 8 9 11 12 14 18 21 22 24 28 33 36 42 44 56 63 66 72 77 84 88 97 99 126 132 154 168 194 198 231 252 264 291 308 388 396 462 504 582 616 679 693 776 792 873 924 1,067 1,164 1,358 1,386 1,746 1,848 2,037 2,134

Collatz Trajectory (71 steps to reach 1)

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

537,768 268,884 134,442 67,221 201,664 100,832 50,416 25,208 12,604 6,302 3,151 9,454 4,727 14,182 7,091 21,274 10,637 31,912 15,956 7,978 3,989 11,968 5,984 2,992 1,496 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17

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