108,416

2⁷ × 7 × 11²

Starting at 108,416, the Collatz iteration reaches 1 after 40 steps. The first transition is 54208; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^7 × 7 × 11^2

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 271,320

Proper Divisor Sum 162,904

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #108413 ← → #108421

Radix Representation

Decimal	108416
Binary	11010011110000000 (17 bits)
Octal	0o323600
Hexadecimal	0x1A780

Divisor Catalog (48)

1 2 4 7 8 11 14 16 22 28 32 44 56 64 77 88 112 121 128 154 176 224 242 308 352 448 484 616 704 847 896 968 1,232 1,408 1,694 1,936 2,464 3,388 3,872 4,928 6,776 7,744 9,856 13,552 15,488 27,104 54,208 108,416

Collatz Trajectory (40 steps to reach 1)

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

108,416 54,208 27,104 13,552 6,776 3,388 1,694 847 2,542 1,271 3,814 1,907 5,722 2,861 8,584 4,292 2,146 1,073 3,220 1,610 805 2,416 1,208 604 302 151 454 227 682 341 1,024 512 256 128 64 32 16 8 4 2 1

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