80,762

2 × 11 × 3671

Starting at 80,762, the Collatz iteration reaches 1 after 151 steps. The first transition is 40381; the starting value is even with 8 positive divisors.

Prime Factor Structure

Factorization String 2 × 11 × 3671

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 132,192

Proper Divisor Sum 51,430

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #80761 ← → #80777

Radix Representation

Decimal	80762
Binary	10011101101111010 (17 bits)
Octal	0o235572
Hexadecimal	0x13B7A

Divisor Catalog (8)

1 2 11 22 3,671 7,342 40,381 80,762

Collatz Trajectory (151 steps to reach 1)

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

80,762 40,381 121,144 60,572 30,286 15,143 45,430 22,715 68,146 34,073 102,220 51,110 25,555 76,666 38,333 115,000 57,500 28,750 14,375 43,126 21,563 64,690 32,345 97,036 48,518 24,259 72,778 36,389 109,168 54,584 27,292 13,646 6,823 20,470 10,235 30,706 15,353 46,060 23,030 11,515 34,546 17,273 51,820 25,910 12,955 38,866 19,433 58,300 29,150 14,575 43,726 21,863 65,590 32,795 98,386 49,193 147,580 73,790 36,895 110,686

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