829,459

103 × 8053

Starting at 829,459, the Collatz iteration reaches 1 after 175 steps. The first transition is 2488378; the starting value is odd with 4 positive divisors.

Prime Factor Structure

Factorization String 103 × 8053

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 4

Divisor Sum (σ) 837,616

Proper Divisor Sum 8,157

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #829457 ← → #829463

Radix Representation

Decimal	829459
Binary	11001010100000010011 (20 bits)
Octal	0o3124023
Hexadecimal	0xCA813

Divisor Catalog (4)

1 103 8,053 829,459

Collatz Trajectory (175 steps to reach 1)

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

829,459 2,488,378 1,244,189 3,732,568 1,866,284 933,142 466,571 1,399,714 699,857 2,099,572 1,049,786 524,893 1,574,680 787,340 393,670 196,835 590,506 295,253 885,760 442,880 221,440 110,720 55,360 27,680 13,840 6,920 3,460 1,730 865 2,596 1,298 649 1,948 974 487 1,462 731 2,194 1,097 3,292 1,646 823 2,470 1,235 3,706 1,853 5,560 2,780 1,390 695 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587 1,762 881

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