782,023

11² × 23 × 281

Starting at 782,023, the Collatz iteration reaches 1 after 224 steps. The first transition is 2346070; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 11^2 × 23 × 281

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 900,144

Proper Divisor Sum 118,121

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #782011 ← → #782053

Radix Representation

Decimal	782023
Binary	10111110111011000111 (20 bits)
Octal	0o2767307
Hexadecimal	0xBEEC7

Divisor Catalog (12)

1 11 23 121 253 281 2,783 3,091 6,463 34,001 71,093 782,023

Collatz Trajectory (224 steps to reach 1)

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

782,023 2,346,070 1,173,035 3,519,106 1,759,553 5,278,660 2,639,330 1,319,665 3,958,996 1,979,498 989,749 2,969,248 1,484,624 742,312 371,156 185,578 92,789 278,368 139,184 69,592 34,796 17,398 8,699 26,098 13,049 39,148 19,574 9,787 29,362 14,681 44,044 22,022 11,011 33,034 16,517 49,552 24,776 12,388 6,194 3,097 9,292 4,646 2,323 6,970 3,485 10,456 5,228 2,614 1,307 3,922 1,961 5,884 2,942 1,471 4,414 2,207 6,622 3,311 9,934 4,967

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