8,237,306

2 × 7 × 11 × 89 × 601

Starting at 8,237,306, the Collatz iteration reaches 1 after 217 steps. The first transition is 4118653; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 7 × 11 × 89 × 601

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 15,603,840

Proper Divisor Sum 7,366,534

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #8237303 ← → #8237309

Radix Representation

Decimal	8237306
Binary	11111011011000011111010 (23 bits)
Octal	0o37330372
Hexadecimal	0x7DB0FA

Divisor Catalog (32)

1 2 7 11 14 22 77 89 154 178 601 623 979 1,202 1,246 1,958 4,207 6,611 6,853 8,414 13,222 13,706 46,277 53,489 92,554 106,978 374,423 588,379 748,846 1,176,758 4,118,653 8,237,306

Collatz Trajectory (217 steps to reach 1)

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

8,237,306 4,118,653 12,355,960 6,177,980 3,088,990 1,544,495 4,633,486 2,316,743 6,950,230 3,475,115 10,425,346 5,212,673 15,638,020 7,819,010 3,909,505 11,728,516 5,864,258 2,932,129 8,796,388 4,398,194 2,199,097 6,597,292 3,298,646 1,649,323 4,947,970 2,473,985 7,421,956 3,710,978 1,855,489 5,566,468 2,783,234 1,391,617 4,174,852 2,087,426 1,043,713 3,131,140 1,565,570 782,785 2,348,356 1,174,178 587,089 1,761,268 880,634 440,317 1,320,952 660,476 330,238 165,119 495,358 247,679 743,038 371,519 1,114,558 557,279 1,671,838 835,919 2,507,758 1,253,879 3,761,638 1,880,819

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