8,837,829

3⁴ × 7 × 11 × 13 × 109

Starting at 8,837,829, the Collatz iteration reaches 1 after 75 steps. The first transition is 26513488; the starting value is odd with 80 positive divisors.

Prime Factor Structure

Factorization String 3^4 × 7 × 11 × 13 × 109

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 17,888,640

Proper Divisor Sum 9,050,811

Digit Sum / Digital Root 45 (Root: 9)

Adjacent Primes #8837827 ← → #8837861

Radix Representation

Decimal	8837829
Binary	100001101101101011000101 (24 bits)
Octal	0o41555305
Hexadecimal	0x86DAC5

Divisor Catalog (60 of 80)

1 3 7 9 11 13 21 27 33 39 63 77 81 91 99 109 117 143 189 231 273 297 327 351 429 567 693 763 819 891 981 1,001 1,053 1,199 1,287 1,417 2,079 2,289 2,457 2,943 3,003 3,597 3,861 4,251 6,237 6,867 7,371 8,393 8,829 9,009 9,919 10,791 11,583 12,753 15,587 20,601 25,179 27,027 29,757 32,373

Collatz Trajectory (75 steps to reach 1)

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

8,837,829 26,513,488 13,256,744 6,628,372 3,314,186 1,657,093 4,971,280 2,485,640 1,242,820 621,410 310,705 932,116 466,058 233,029 699,088 349,544 174,772 87,386 43,693 131,080 65,540 32,770 16,385 49,156 24,578 12,289 36,868 18,434 9,217 27,652 13,826 6,913 20,740 10,370 5,185 15,556 7,778 3,889 11,668 5,834 2,917 8,752 4,376 2,188 1,094 547 1,642 821 2,464 1,232 616 308 154 77 232 116 58 29 88 44

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