76,791

3 × 11 × 13 × 179

Starting at 76,791, the Collatz iteration reaches 1 after 81 steps. The first transition is 230374; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 11 × 13 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 120,960

Proper Divisor Sum 44,169

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #76781 ← → #76801

Radix Representation

Decimal	76791
Binary	10010101111110111 (17 bits)
Octal	0o225767
Hexadecimal	0x12BF7

Divisor Catalog (16)

1 3 11 13 33 39 143 179 429 537 1,969 2,327 5,907 6,981 25,597 76,791

Collatz Trajectory (81 steps to reach 1)

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

76,791 230,374 115,187 345,562 172,781 518,344 259,172 129,586 64,793 194,380 97,190 48,595 145,786 72,893 218,680 109,340 54,670 27,335 82,006 41,003 123,010 61,505 184,516 92,258 46,129 138,388 69,194 34,597 103,792 51,896 25,948 12,974 6,487 19,462 9,731 29,194 14,597 43,792 21,896 10,948 5,474 2,737 8,212 4,106 2,053 6,160 3,080 1,540 770 385 1,156 578 289 868 434 217 652 326 163 490

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