77,920

2⁵ × 5 × 487

Starting at 77,920, the Collatz iteration reaches 1 after 138 steps. The first transition is 38960; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 5 × 487

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 184,464

Proper Divisor Sum 106,544

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #77899 ← → #77929

Radix Representation

Decimal	77920
Binary	10011000001100000 (17 bits)
Octal	0o230140
Hexadecimal	0x13060

Divisor Catalog (24)

1 2 4 5 8 10 16 20 32 40 80 160 487 974 1,948 2,435 3,896 4,870 7,792 9,740 15,584 19,480 38,960 77,920

Collatz Trajectory (138 steps to reach 1)

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

77,920 38,960 19,480 9,740 4,870 2,435 7,306 3,653 10,960 5,480 2,740 1,370 685 2,056 1,028 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526

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