447,615

3² × 5 × 7³ × 29

447,615 factors as 3^2 × 5 × 7^3 × 29. Its 48 positive divisors give a proper-divisor sum of 488,385, so this integer is abundant. The Collatz stopping time is 187 steps.

Prime Factor Structure

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

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 936,000

Proper Divisor Sum 488,385

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #447611 ← → #447617

Radix Representation

Decimal	447615
Binary	1101101010001111111 (19 bits)
Octal	0o1552177
Hexadecimal	0x6D47F

Divisor Catalog (48)

1 3 5 7 9 15 21 29 35 45 49 63 87 105 145 147 203 245 261 315 343 435 441 609 735 1,015 1,029 1,305 1,421 1,715 1,827 2,205 3,045 3,087 4,263 5,145 7,105 9,135 9,947 12,789 15,435 21,315 29,841 49,735 63,945 89,523 149,205 447,615

Collatz Trajectory (187 steps to reach 1)

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

447,615 1,342,846 671,423 2,014,270 1,007,135 3,021,406 1,510,703 4,532,110 2,266,055 6,798,166 3,399,083 10,197,250 5,098,625 15,295,876 7,647,938 3,823,969 11,471,908 5,735,954 2,867,977 8,603,932 4,301,966 2,150,983 6,452,950 3,226,475 9,679,426 4,839,713 14,519,140 7,259,570 3,629,785 10,889,356 5,444,678 2,722,339 8,167,018 4,083,509 12,250,528 6,125,264 3,062,632 1,531,316 765,658 382,829 1,148,488 574,244 287,122 143,561 430,684 215,342 107,671 323,014 161,507 484,522 242,261 726,784 363,392 181,696 90,848 45,424 22,712 11,356 5,678 2,839

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