6,827,436

2² × 3³ × 7 × 11 × 821

Starting at 6,827,436, the Collatz iteration reaches 1 after 147 steps. The first transition is 3413718; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 7 × 11 × 821

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 22,095,360

Proper Divisor Sum 15,267,924

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #6827413 ← → #6827449

Radix Representation

Decimal	6827436
Binary	11010000010110110101100 (23 bits)
Octal	0o32026654
Hexadecimal	0x682DAC

Divisor Catalog (60 of 96)

1 2 3 4 6 7 9 11 12 14 18 21 22 27 28 33 36 42 44 54 63 66 77 84 99 108 126 132 154 189 198 231 252 297 308 378 396 462 594 693 756 821 924 1,188 1,386 1,642 2,079 2,463 2,772 3,284 4,158 4,926 5,747 7,389 8,316 9,031 9,852 11,494 14,778 17,241

Collatz Trajectory (147 steps to reach 1)

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

6,827,436 3,413,718 1,706,859 5,120,578 2,560,289 7,680,868 3,840,434 1,920,217 5,760,652 2,880,326 1,440,163 4,320,490 2,160,245 6,480,736 3,240,368 1,620,184 810,092 405,046 202,523 607,570 303,785 911,356 455,678 227,839 683,518 341,759 1,025,278 512,639 1,537,918 768,959 2,306,878 1,153,439 3,460,318 1,730,159 5,190,478 2,595,239 7,785,718 3,892,859 11,678,578 5,839,289 17,517,868 8,758,934 4,379,467 13,138,402 6,569,201 19,707,604 9,853,802 4,926,901 14,780,704 7,390,352 3,695,176 1,847,588 923,794 461,897 1,385,692 692,846 346,423 1,039,270 519,635 1,558,906

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