829,409

7 × 47 × 2521

829,409 factors as 7 × 47 × 2521. Its 8 positive divisors give a proper-divisor sum of 139,039, so this integer is deficient. The Collatz stopping time is 113 steps.

Prime Factor Structure

Factorization String 7 × 47 × 2521

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 968,448

Proper Divisor Sum 139,039

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #829399 ← → #829453

Radix Representation

Decimal	829409
Binary	11001010011111100001 (20 bits)
Octal	0o3123741
Hexadecimal	0xCA7E1

Divisor Catalog (8)

1 7 47 329 2,521 17,647 118,487 829,409

Collatz Trajectory (113 steps to reach 1)

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

829,409 2,488,228 1,244,114 622,057 1,866,172 933,086 466,543 1,399,630 699,815 2,099,446 1,049,723 3,149,170 1,574,585 4,723,756 2,361,878 1,180,939 3,542,818 1,771,409 5,314,228 2,657,114 1,328,557 3,985,672 1,992,836 996,418 498,209 1,494,628 747,314 373,657 1,120,972 560,486 280,243 840,730 420,365 1,261,096 630,548 315,274 157,637 472,912 236,456 118,228 59,114 29,557 88,672 44,336 22,168 11,084 5,542 2,771 8,314 4,157 12,472 6,236 3,118 1,559 4,678 2,339 7,018 3,509 10,528 5,264

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