7,759,800

2³ × 3⁴ × 5² × 479

Starting at 7,759,800, the Collatz iteration reaches 1 after 93 steps. The first transition is 3879900; the starting value is even with 120 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^4 × 5^2 × 479

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 27,007,200

Proper Divisor Sum 19,247,400

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7759789 ← → #7759811

Radix Representation

Decimal	7759800
Binary	11101100110011110111000 (23 bits)
Octal	0o35463670
Hexadecimal	0x7667B8

Divisor Catalog (60 of 120)

1 2 3 4 5 6 8 9 10 12 15 18 20 24 25 27 30 36 40 45 50 54 60 72 75 81 90 100 108 120 135 150 162 180 200 216 225 270 300 324 360 405 450 479 540 600 648 675 810 900 958 1,080 1,350 1,437 1,620 1,800 1,916 2,025 2,395 2,700

Collatz Trajectory (93 steps to reach 1)

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

7,759,800 3,879,900 1,939,950 969,975 2,909,926 1,454,963 4,364,890 2,182,445 6,547,336 3,273,668 1,636,834 818,417 2,455,252 1,227,626 613,813 1,841,440 920,720 460,360 230,180 115,090 57,545 172,636 86,318 43,159 129,478 64,739 194,218 97,109 291,328 145,664 72,832 36,416 18,208 9,104 4,552 2,276 1,138 569 1,708 854 427 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834 917 2,752 1,376

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