488,565

3³ × 5 × 7 × 11 × 47

488,565 factors as 3^3 × 5 × 7 × 11 × 47. Its 64 positive divisors give a proper-divisor sum of 617,355, so this integer is abundant. The Collatz stopping time is 195 steps.

Prime Factor Structure

Factorization String 3^3 × 5 × 7 × 11 × 47

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 1,105,920

Proper Divisor Sum 617,355

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #488539 ← → #488567

Radix Representation

Decimal	488565
Binary	1110111010001110101 (19 bits)
Octal	0o1672165
Hexadecimal	0x77475

Divisor Catalog (60 of 64)

1 3 5 7 9 11 15 21 27 33 35 45 47 55 63 77 99 105 135 141 165 189 231 235 297 315 329 385 423 495 517 693 705 945 987 1,155 1,269 1,485 1,551 1,645 2,079 2,115 2,585 2,961 3,465 3,619 4,653 4,935 6,345 7,755 8,883 10,395 10,857 13,959 14,805 18,095 23,265 32,571 44,415 54,285

Collatz Trajectory (195 steps to reach 1)

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

488,565 1,465,696 732,848 366,424 183,212 91,606 45,803 137,410 68,705 206,116 103,058 51,529 154,588 77,294 38,647 115,942 57,971 173,914 86,957 260,872 130,436 65,218 32,609 97,828 48,914 24,457 73,372 36,686 18,343 55,030 27,515 82,546 41,273 123,820 61,910 30,955 92,866 46,433 139,300 69,650 34,825 104,476 52,238 26,119 78,358 39,179 117,538 58,769 176,308 88,154 44,077 132,232 66,116 33,058 16,529 49,588 24,794 12,397 37,192 18,596

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