442,575

3² × 5² × 7 × 281

442,575 factors as 3^2 × 5^2 × 7 × 281. Its 36 positive divisors give a proper-divisor sum of 466,593, so this integer is abundant. The Collatz stopping time is 218 steps.

Prime Factor Structure

Factorization String 3^2 × 5^2 × 7 × 281

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 909,168

Proper Divisor Sum 466,593

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #442573 ← → #442577

Radix Representation

Decimal	442575
Binary	1101100000011001111 (19 bits)
Octal	0o1540317
Hexadecimal	0x6C0CF

Divisor Catalog (36)

1 3 5 7 9 15 21 25 35 45 63 75 105 175 225 281 315 525 843 1,405 1,575 1,967 2,529 4,215 5,901 7,025 9,835 12,645 17,703 21,075 29,505 49,175 63,225 88,515 147,525 442,575

Collatz Trajectory (218 steps to reach 1)

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

442,575 1,327,726 663,863 1,991,590 995,795 2,987,386 1,493,693 4,481,080 2,240,540 1,120,270 560,135 1,680,406 840,203 2,520,610 1,260,305 3,780,916 1,890,458 945,229 2,835,688 1,417,844 708,922 354,461 1,063,384 531,692 265,846 132,923 398,770 199,385 598,156 299,078 149,539 448,618 224,309 672,928 336,464 168,232 84,116 42,058 21,029 63,088 31,544 15,772 7,886 3,943 11,830 5,915 17,746 8,873 26,620 13,310 6,655 19,966 9,983 29,950 14,975 44,926 22,463 67,390 33,695 101,086

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