8,209,320

2³ × 3 × 5 × 7 × 29 × 337

Starting at 8,209,320, the Collatz iteration reaches 1 after 54 steps. The first transition is 4104660; the starting value is even with 128 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 7 × 29 × 337

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 128

Divisor Sum (σ) 29,203,200

Proper Divisor Sum 20,993,880

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #8209303 ← → #8209339

Radix Representation

Decimal	8209320
Binary	11111010100001110101000 (23 bits)
Octal	0o37241650
Hexadecimal	0x7D43A8

Divisor Catalog (60 of 128)

1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 28 29 30 35 40 42 56 58 60 70 84 87 105 116 120 140 145 168 174 203 210 232 280 290 337 348 406 420 435 580 609 674 696 812 840 870 1,011 1,015 1,160 1,218 1,348 1,624 1,685 1,740 2,022

Collatz Trajectory (54 steps to reach 1)

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

8,209,320 4,104,660 2,052,330 1,026,165 3,078,496 1,539,248 769,624 384,812 192,406 96,203 288,610 144,305 432,916 216,458 108,229 324,688 162,344 81,172 40,586 20,293 60,880 30,440 15,220 7,610 3,805 11,416 5,708 2,854 1,427 4,282 2,141 6,424 3,212 1,606 803 2,410 1,205 3,616 1,808 904 452 226 113 340 170 85 256 128 64 32 16 8 4 2 1

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