8,212,347

3⁴ × 11 × 13 × 709

Starting at 8,212,347, the Collatz iteration reaches 1 after 137 steps. The first transition is 24637042; the starting value is odd with 40 positive divisors.

Prime Factor Structure

Factorization String 3^4 × 11 × 13 × 709

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 14,432,880

Proper Divisor Sum 6,220,533

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8212333 ← → #8212363

Radix Representation

Decimal	8212347
Binary	11111010100111101111011 (23 bits)
Octal	0o37247573
Hexadecimal	0x7D4F7B

Divisor Catalog (40)

1 3 9 11 13 27 33 39 81 99 117 143 297 351 429 709 891 1,053 1,287 2,127 3,861 6,381 7,799 9,217 11,583 19,143 23,397 27,651 57,429 70,191 82,953 101,387 210,573 248,859 304,161 631,719 746,577 912,483 2,737,449 8,212,347

Collatz Trajectory (137 steps to reach 1)

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

8,212,347 24,637,042 12,318,521 36,955,564 18,477,782 9,238,891 27,716,674 13,858,337 41,575,012 20,787,506 10,393,753 31,181,260 15,590,630 7,795,315 23,385,946 11,692,973 35,078,920 17,539,460 8,769,730 4,384,865 13,154,596 6,577,298 3,288,649 9,865,948 4,932,974 2,466,487 7,399,462 3,699,731 11,099,194 5,549,597 16,648,792 8,324,396 4,162,198 2,081,099 6,243,298 3,121,649 9,364,948 4,682,474 2,341,237 7,023,712 3,511,856 1,755,928 877,964 438,982 219,491 658,474 329,237 987,712 493,856 246,928 123,464 61,732 30,866 15,433 46,300 23,150 11,575 34,726 17,363 52,090

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