223,728

2⁴ × 3 × 59 × 79

Starting at 223,728, the Collatz iteration reaches 1 after 98 steps. The first transition is 111864; the starting value is even with 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 59 × 79

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 595,200

Proper Divisor Sum 371,472

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #223711 ← → #223747

Radix Representation

Decimal	223728
Binary	110110100111110000 (18 bits)
Octal	0o664760
Hexadecimal	0x369F0

Divisor Catalog (40)

1 2 3 4 6 8 12 16 24 48 59 79 118 158 177 236 237 316 354 472 474 632 708 944 948 1,264 1,416 1,896 2,832 3,792 4,661 9,322 13,983 18,644 27,966 37,288 55,932 74,576 111,864 223,728

Collatz Trajectory (98 steps to reach 1)

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

223,728 111,864 55,932 27,966 13,983 41,950 20,975 62,926 31,463 94,390 47,195 141,586 70,793 212,380 106,190 53,095 159,286 79,643 238,930 119,465 358,396 179,198 89,599 268,798 134,399 403,198 201,599 604,798 302,399 907,198 453,599 1,360,798 680,399 2,041,198 1,020,599 3,061,798 1,530,899 4,592,698 2,296,349 6,889,048 3,444,524 1,722,262 861,131 2,583,394 1,291,697 3,875,092 1,937,546 968,773 2,906,320 1,453,160 726,580 363,290 181,645 544,936 272,468 136,234 68,117 204,352 102,176 51,088

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