223,767

3² × 23² × 47

223,767 has the prime decomposition 3^2 × 23^2 × 47. Its 3 distinct prime factors produce 18 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 23^2 × 47

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 18

Divisor Sum (σ) 345,072

Proper Divisor Sum 121,305

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #223759 ← → #223781

Radix Representation

Decimal	223767
Binary	110110101000010111 (18 bits)
Octal	0o665027
Hexadecimal	0x36A17

Divisor Catalog (18)

1 3 9 23 47 69 141 207 423 529 1,081 1,587 3,243 4,761 9,729 24,863 74,589 223,767

Collatz Trajectory (93 steps to reach 1)

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

223,767 671,302 335,651 1,006,954 503,477 1,510,432 755,216 377,608 188,804 94,402 47,201 141,604 70,802 35,401 106,204 53,102 26,551 79,654 39,827 119,482 59,741 179,224 89,612 44,806 22,403 67,210 33,605 100,816 50,408 25,204 12,602 6,301 18,904 9,452 4,726 2,363 7,090 3,545 10,636 5,318 2,659 7,978 3,989 11,968 5,984 2,992 1,496 748 374 187 562 281 844 422 211 634 317 952 476 238

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