459,840

2⁶ × 3 × 5 × 479

459,840 factors as 2^6 × 3 × 5 × 479. Its 56 positive divisors give a proper-divisor sum of 1,003,200, so this integer is abundant. The Collatz stopping time is 76 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 5 × 479

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 56

Divisor Sum (σ) 1,463,040

Proper Divisor Sum 1,003,200

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #459829 ← → #459841

Radix Representation

Decimal	459840
Binary	1110000010001000000 (19 bits)
Octal	0o1602100
Hexadecimal	0x70440

Divisor Catalog (56)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 64 80 96 120 160 192 240 320 479 480 958 960 1,437 1,916 2,395 2,874 3,832 4,790 5,748 7,185 7,664 9,580 11,496 14,370 15,328 19,160 22,992 28,740 30,656 38,320 45,984 57,480 76,640 91,968 114,960 153,280 229,920 459,840

Collatz Trajectory (76 steps to reach 1)

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

459,840 229,920 114,960 57,480 28,740 14,370 7,185 21,556 10,778 5,389 16,168 8,084 4,042 2,021 6,064 3,032 1,516 758 379 1,138 569 1,708 854 427 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834 917 2,752 1,376 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14

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