828,541

7² × 37 × 457

828,541 factors as 7^2 × 37 × 457. Its 12 positive divisors give a proper-divisor sum of 163,487, so this integer is deficient. The Collatz stopping time is 113 steps.

Prime Factor Structure

Factorization String 7^2 × 37 × 457

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 992,028

Proper Divisor Sum 163,487

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #828523 ← → #828547

Radix Representation

Decimal	828541
Binary	11001010010001111101 (20 bits)
Octal	0o3122175
Hexadecimal	0xCA47D

Divisor Catalog (12)

1 7 37 49 259 457 1,813 3,199 16,909 22,393 118,363 828,541

Collatz Trajectory (113 steps to reach 1)

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

828,541 2,485,624 1,242,812 621,406 310,703 932,110 466,055 1,398,166 699,083 2,097,250 1,048,625 3,145,876 1,572,938 786,469 2,359,408 1,179,704 589,852 294,926 147,463 442,390 221,195 663,586 331,793 995,380 497,690 248,845 746,536 373,268 186,634 93,317 279,952 139,976 69,988 34,994 17,497 52,492 26,246 13,123 39,370 19,685 59,056 29,528 14,764 7,382 3,691 11,074 5,537 16,612 8,306 4,153 12,460 6,230 3,115 9,346 4,673 14,020 7,010 3,505 10,516 5,258

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