7,878,024

2³ × 3² × 7³ × 11 × 29

Starting at 7,878,024, the Collatz iteration reaches 1 after 186 steps. The first transition is 3939012; the starting value is even with 192 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 7^3 × 11 × 29

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 192

Divisor Sum (σ) 28,080,000

Proper Divisor Sum 20,201,976

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7878023 ← → #7878037

Radix Representation

Decimal	7878024
Binary	11110000011010110001000 (23 bits)
Octal	0o36032610
Hexadecimal	0x783588

Divisor Catalog (60 of 192)

1 2 3 4 6 7 8 9 11 12 14 18 21 22 24 28 29 33 36 42 44 49 56 58 63 66 72 77 84 87 88 98 99 116 126 132 147 154 168 174 196 198 203 231 232 252 261 264 294 308 319 343 348 392 396 406 441 462 504 522

Collatz Trajectory (186 steps to reach 1)

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

7,878,024 3,939,012 1,969,506 984,753 2,954,260 1,477,130 738,565 2,215,696 1,107,848 553,924 276,962 138,481 415,444 207,722 103,861 311,584 155,792 77,896 38,948 19,474 9,737 29,212 14,606 7,303 21,910 10,955 32,866 16,433 49,300 24,650 12,325 36,976 18,488 9,244 4,622 2,311 6,934 3,467 10,402 5,201 15,604 7,802 3,901 11,704 5,852 2,926 1,463 4,390 2,195 6,586 3,293 9,880 4,940 2,470 1,235 3,706 1,853 5,560 2,780 1,390

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