829,207

37 × 73 × 307

Starting at 829,207, the Collatz iteration reaches 1 after 162 steps. The first transition is 2487622; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 37 × 73 × 307

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 866,096

Proper Divisor Sum 36,889

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #829193 ← → #829211

Radix Representation

Decimal	829207
Binary	11001010011100010111 (20 bits)
Octal	0o3123427
Hexadecimal	0xCA717

Divisor Catalog (8)

1 37 73 307 2,701 11,359 22,411 829,207

Collatz Trajectory (162 steps to reach 1)

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

829,207 2,487,622 1,243,811 3,731,434 1,865,717 5,597,152 2,798,576 1,399,288 699,644 349,822 174,911 524,734 262,367 787,102 393,551 1,180,654 590,327 1,770,982 885,491 2,656,474 1,328,237 3,984,712 1,992,356 996,178 498,089 1,494,268 747,134 373,567 1,120,702 560,351 1,681,054 840,527 2,521,582 1,260,791 3,782,374 1,891,187 5,673,562 2,836,781 8,510,344 4,255,172 2,127,586 1,063,793 3,191,380 1,595,690 797,845 2,393,536 1,196,768 598,384 299,192 149,596 74,798 37,399 112,198 56,099 168,298 84,149 252,448 126,224 63,112 31,556

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