272,496

2⁴ × 3 × 7 × 811

Starting at 272,496, the Collatz iteration reaches 1 after 83 steps. The first transition is 136248; the starting value is even with 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 7 × 811

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 805,504

Proper Divisor Sum 533,008

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #272477 ← → #272507

Radix Representation

Decimal	272496
Binary	1000010100001110000 (19 bits)
Octal	0o1024160
Hexadecimal	0x42870

Divisor Catalog (40)

1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 56 84 112 168 336 811 1,622 2,433 3,244 4,866 5,677 6,488 9,732 11,354 12,976 17,031 19,464 22,708 34,062 38,928 45,416 68,124 90,832 136,248 272,496

Collatz Trajectory (83 steps to reach 1)

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

272,496 136,248 68,124 34,062 17,031 51,094 25,547 76,642 38,321 114,964 57,482 28,741 86,224 43,112 21,556 10,778 5,389 16,168 8,084 4,042 2,021 6,064 3,032 1,516 758 379 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 1,376 688 344 172 86 43 130 65 196 98 49

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