6,821,600

2⁵ × 5² × 8527

Starting at 6,821,600, the Collatz iteration reaches 1 after 116 steps. The first transition is 3410800; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 5^2 × 8527

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 16,655,184

Proper Divisor Sum 9,833,584

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #6821599 ← → #6821611

Radix Representation

Decimal	6821600
Binary	11010000001011011100000 (23 bits)
Octal	0o32013340
Hexadecimal	0x6816E0

Divisor Catalog (36)

1 2 4 5 8 10 16 20 25 32 40 50 80 100 160 200 400 800 8,527 17,054 34,108 42,635 68,216 85,270 136,432 170,540 213,175 272,864 341,080 426,350 682,160 852,700 1,364,320 1,705,400 3,410,800 6,821,600

Collatz Trajectory (116 steps to reach 1)

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

6,821,600 3,410,800 1,705,400 852,700 426,350 213,175 639,526 319,763 959,290 479,645 1,438,936 719,468 359,734 179,867 539,602 269,801 809,404 404,702 202,351 607,054 303,527 910,582 455,291 1,365,874 682,937 2,048,812 1,024,406 512,203 1,536,610 768,305 2,304,916 1,152,458 576,229 1,728,688 864,344 432,172 216,086 108,043 324,130 162,065 486,196 243,098 121,549 364,648 182,324 91,162 45,581 136,744 68,372 34,186 17,093 51,280 25,640 12,820 6,410 3,205 9,616 4,808 2,404 1,202

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