7,826,025

3 × 5² × 104347

Starting at 7,826,025, the Collatz iteration reaches 1 after 186 steps. The first transition is 23478076; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 104347

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 12,939,152

Proper Divisor Sum 5,113,127

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7826023 ← → #7826047

Radix Representation

Decimal	7826025
Binary	11101110110101001101001 (23 bits)
Octal	0o35665151
Hexadecimal	0x776A69

Divisor Catalog (12)

1 3 5 15 25 75 104,347 313,041 521,735 1,565,205 2,608,675 7,826,025

Collatz Trajectory (186 steps to reach 1)

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

7,826,025 23,478,076 11,739,038 5,869,519 17,608,558 8,804,279 26,412,838 13,206,419 39,619,258 19,809,629 59,428,888 29,714,444 14,857,222 7,428,611 22,285,834 11,142,917 33,428,752 16,714,376 8,357,188 4,178,594 2,089,297 6,267,892 3,133,946 1,566,973 4,700,920 2,350,460 1,175,230 587,615 1,762,846 881,423 2,644,270 1,322,135 3,966,406 1,983,203 5,949,610 2,974,805 8,924,416 4,462,208 2,231,104 1,115,552 557,776 278,888 139,444 69,722 34,861 104,584 52,292 26,146 13,073 39,220 19,610 9,805 29,416 14,708 7,354 3,677 11,032 5,516 2,758 1,379

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