464,640

2⁸ × 3 × 5 × 11²

Starting at 464,640, the Collatz iteration reaches 1 after 63 steps. The first transition is 232320; the starting value is even with 108 positive divisors.

Prime Factor Structure

Factorization String 2^8 × 3 × 5 × 11^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 108

Divisor Sum (σ) 1,631,112

Proper Divisor Sum 1,166,472

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #464621 ← → #464647

Radix Representation

Decimal	464640
Binary	1110001011100000000 (19 bits)
Octal	0o1613400
Hexadecimal	0x71700

Divisor Catalog (60 of 108)

1 2 3 4 5 6 8 10 11 12 15 16 20 22 24 30 32 33 40 44 48 55 60 64 66 80 88 96 110 120 121 128 132 160 165 176 192 220 240 242 256 264 320 330 352 363 384 440 480 484 528 605 640 660 704 726 768 880 960 968

Collatz Trajectory (63 steps to reach 1)

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

464,640 232,320 116,160 58,080 29,040 14,520 7,260 3,630 1,815 5,446 2,723 8,170 4,085 12,256 6,128 3,064 1,532 766 383 1,150 575 1,726 863 2,590 1,295 3,886 1,943 5,830 2,915 8,746 4,373 13,120 6,560 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16

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