7,739,544

2³ × 3 × 389 × 829

Starting at 7,739,544, the Collatz iteration reaches 1 after 186 steps. The first transition is 3869772; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 389 × 829

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 19,422,000

Proper Divisor Sum 11,682,456

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #7739531 ← → #7739581

Radix Representation

Decimal	7739544
Binary	11101100001100010011000 (23 bits)
Octal	0o35414230
Hexadecimal	0x761898

Divisor Catalog (32)

1 2 3 4 6 8 12 24 389 778 829 1,167 1,556 1,658 2,334 2,487 3,112 3,316 4,668 4,974 6,632 9,336 9,948 19,896 322,481 644,962 967,443 1,289,924 1,934,886 2,579,848 3,869,772 7,739,544

Collatz Trajectory (186 steps to reach 1)

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

7,739,544 3,869,772 1,934,886 967,443 2,902,330 1,451,165 4,353,496 2,176,748 1,088,374 544,187 1,632,562 816,281 2,448,844 1,224,422 612,211 1,836,634 918,317 2,754,952 1,377,476 688,738 344,369 1,033,108 516,554 258,277 774,832 387,416 193,708 96,854 48,427 145,282 72,641 217,924 108,962 54,481 163,444 81,722 40,861 122,584 61,292 30,646 15,323 45,970 22,985 68,956 34,478 17,239 51,718 25,859 77,578 38,789 116,368 58,184 29,092 14,546 7,273 21,820 10,910 5,455 16,366 8,183

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