7,785,275

5² × 89 × 3499

Starting at 7,785,275, the Collatz iteration reaches 1 after 178 steps. The first transition is 23355826; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 5^2 × 89 × 3499

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 9,765,000

Proper Divisor Sum 1,979,725

Digit Sum / Digital Root 41 (Root: 5)

Adjacent Primes #7785259 ← → #7785277

Radix Representation

Decimal	7785275
Binary	11101101100101100111011 (23 bits)
Octal	0o35545473
Hexadecimal	0x76CB3B

Divisor Catalog (12)

1 5 25 89 445 2,225 3,499 17,495 87,475 311,411 1,557,055 7,785,275

Collatz Trajectory (178 steps to reach 1)

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

7,785,275 23,355,826 11,677,913 35,033,740 17,516,870 8,758,435 26,275,306 13,137,653 39,412,960 19,706,480 9,853,240 4,926,620 2,463,310 1,231,655 3,694,966 1,847,483 5,542,450 2,771,225 8,313,676 4,156,838 2,078,419 6,235,258 3,117,629 9,352,888 4,676,444 2,338,222 1,169,111 3,507,334 1,753,667 5,261,002 2,630,501 7,891,504 3,945,752 1,972,876 986,438 493,219 1,479,658 739,829 2,219,488 1,109,744 554,872 277,436 138,718 69,359 208,078 104,039 312,118 156,059 468,178 234,089 702,268 351,134 175,567 526,702 263,351 790,054 395,027 1,185,082 592,541 1,777,624

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