802,334

2 × 13 × 30859

Starting at 802,334, the Collatz iteration reaches 1 after 69 steps. The first transition is 401167; the starting value is even with 8 positive divisors.

Prime Factor Structure

Factorization String 2 × 13 × 30859

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 1,296,120

Proper Divisor Sum 493,786

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #802331 ← → #802339

Radix Representation

Decimal	802334
Binary	11000011111000011110 (20 bits)
Octal	0o3037036
Hexadecimal	0xC3E1E

Divisor Catalog (8)

1 2 13 26 30,859 61,718 401,167 802,334

Collatz Trajectory (69 steps to reach 1)

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

802,334 401,167 1,203,502 601,751 1,805,254 902,627 2,707,882 1,353,941 4,061,824 2,030,912 1,015,456 507,728 253,864 126,932 63,466 31,733 95,200 47,600 23,800 11,900 5,950 2,975 8,926 4,463 13,390 6,695 20,086 10,043 30,130 15,065 45,196 22,598 11,299 33,898 16,949 50,848 25,424 12,712 6,356 3,178 1,589 4,768 2,384 1,192 596 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26

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