120,398

2 × 37 × 1627

Starting at 120,398, the Collatz iteration reaches 1 after 66 steps. The first transition is 60199; the starting value is even with 8 positive divisors.

Prime Factor Structure

Factorization String 2 × 37 × 1627

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 185,592

Proper Divisor Sum 65,194

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #120397 ← → #120401

Radix Representation

Decimal	120398
Binary	11101011001001110 (17 bits)
Octal	0o353116
Hexadecimal	0x1D64E

Divisor Catalog (8)

1 2 37 74 1,627 3,254 60,199 120,398

Collatz Trajectory (66 steps to reach 1)

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

120,398 60,199 180,598 90,299 270,898 135,449 406,348 203,174 101,587 304,762 152,381 457,144 228,572 114,286 57,143 171,430 85,715 257,146 128,573 385,720 192,860 96,430 48,215 144,646 72,323 216,970 108,485 325,456 162,728 81,364 40,682 20,341 61,024 30,512 15,256 7,628 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

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