173,565

3² × 5 × 7 × 19 × 29

173,565 factors as 3^2 × 5 × 7 × 19 × 29. Its 48 positive divisors give a proper-divisor sum of 200,835, so this integer is abundant. The Collatz stopping time is 77 steps.

Prime Factor Structure

Factorization String 3^2 × 5 × 7 × 19 × 29

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 374,400

Proper Divisor Sum 200,835

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #173561 ← → #173573

Radix Representation

Decimal	173565
Binary	101010010111111101 (18 bits)
Octal	0o522775
Hexadecimal	0x2A5FD

Divisor Catalog (48)

1 3 5 7 9 15 19 21 29 35 45 57 63 87 95 105 133 145 171 203 261 285 315 399 435 551 609 665 855 1,015 1,197 1,305 1,653 1,827 1,995 2,755 3,045 3,857 4,959 5,985 8,265 9,135 11,571 19,285 24,795 34,713 57,855 173,565

Collatz Trajectory (77 steps to reach 1)

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

173,565 520,696 260,348 130,174 65,087 195,262 97,631 292,894 146,447 439,342 219,671 659,014 329,507 988,522 494,261 1,482,784 741,392 370,696 185,348 92,674 46,337 139,012 69,506 34,753 104,260 52,130 26,065 78,196 39,098 19,549 58,648 29,324 14,662 7,331 21,994 10,997 32,992 16,496 8,248 4,124 2,062 1,031 3,094 1,547 4,642 2,321 6,964 3,482 1,741 5,224 2,612 1,306 653 1,960 980 490 245 736 368 184

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