7,823,109

3 × 7 × 401 × 929

Starting at 7,823,109, the Collatz iteration reaches 1 after 186 steps. The first transition is 23469328; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 7 × 401 × 929

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 11,963,520

Proper Divisor Sum 4,140,411

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7823099 ← → #7823113

Radix Representation

Decimal	7823109
Binary	11101110101111100000101 (23 bits)
Octal	0o35657405
Hexadecimal	0x775F05

Divisor Catalog (16)

1 3 7 21 401 929 1,203 2,787 2,807 6,503 8,421 19,509 372,529 1,117,587 2,607,703 7,823,109

Collatz Trajectory (186 steps to reach 1)

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

7,823,109 23,469,328 11,734,664 5,867,332 2,933,666 1,466,833 4,400,500 2,200,250 1,100,125 3,300,376 1,650,188 825,094 412,547 1,237,642 618,821 1,856,464 928,232 464,116 232,058 116,029 348,088 174,044 87,022 43,511 130,534 65,267 195,802 97,901 293,704 146,852 73,426 36,713 110,140 55,070 27,535 82,606 41,303 123,910 61,955 185,866 92,933 278,800 139,400 69,700 34,850 17,425 52,276 26,138 13,069 39,208 19,604 9,802 4,901 14,704 7,352 3,676 1,838 919 2,758 1,379

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