440,496

2⁴ × 3² × 7 × 19 × 23

440,496 factors as 2^4 × 3^2 × 7 × 19 × 23. Its 120 positive divisors give a proper-divisor sum of 1,107,024, so this integer is abundant. The Collatz stopping time is 125 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 7 × 19 × 23

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 1,547,520

Proper Divisor Sum 1,107,024

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #440471 ← → #440497

Radix Representation

Decimal	440496
Binary	1101011100010110000 (19 bits)
Octal	0o1534260
Hexadecimal	0x6B8B0

Divisor Catalog (60 of 120)

1 2 3 4 6 7 8 9 12 14 16 18 19 21 23 24 28 36 38 42 46 48 56 57 63 69 72 76 84 92 112 114 126 133 138 144 152 161 168 171 184 207 228 252 266 276 304 322 336 342 368 399 414 437 456 483 504 532 552 644

Collatz Trajectory (125 steps to reach 1)

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

440,496 220,248 110,124 55,062 27,531 82,594 41,297 123,892 61,946 30,973 92,920 46,460 23,230 11,615 34,846 17,423 52,270 26,135 78,406 39,203 117,610 58,805 176,416 88,208 44,104 22,052 11,026 5,513 16,540 8,270 4,135 12,406 6,203 18,610 9,305 27,916 13,958 6,979 20,938 10,469 31,408 15,704 7,852 3,926 1,963 5,890 2,945 8,836 4,418 2,209 6,628 3,314 1,657 4,972 2,486 1,243 3,730 1,865 5,596 2,798

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