7,732,368

2⁴ × 3³ × 7 × 2557

Starting at 7,732,368, the Collatz iteration reaches 1 after 217 steps. The first transition is 3866184; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 7 × 2557

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 25,375,360

Proper Divisor Sum 17,642,992

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7732343 ← → #7732391

Radix Representation

Decimal	7732368
Binary	11101011111110010010000 (23 bits)
Octal	0o35376220
Hexadecimal	0x75FC90

Divisor Catalog (60 of 80)

1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 36 42 48 54 56 63 72 84 108 112 126 144 168 189 216 252 336 378 432 504 756 1,008 1,512 2,557 3,024 5,114 7,671 10,228 15,342 17,899 20,456 23,013 30,684 35,798 40,912 46,026 53,697 61,368 69,039 71,596 92,052 107,394 122,736 138,078

Collatz Trajectory (217 steps to reach 1)

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

7,732,368 3,866,184 1,933,092 966,546 483,273 1,449,820 724,910 362,455 1,087,366 543,683 1,631,050 815,525 2,446,576 1,223,288 611,644 305,822 152,911 458,734 229,367 688,102 344,051 1,032,154 516,077 1,548,232 774,116 387,058 193,529 580,588 290,294 145,147 435,442 217,721 653,164 326,582 163,291 489,874 244,937 734,812 367,406 183,703 551,110 275,555 826,666 413,333 1,240,000 620,000 310,000 155,000 77,500 38,750 19,375 58,126 29,063 87,190 43,595 130,786 65,393 196,180 98,090 49,045

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