465,600

2⁶ × 3 × 5² × 97

Prime Factor Structure

Factorization String 2^6 × 3 × 5^2 × 97

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 84

Divisor Sum (σ) 1,543,304

Proper Divisor Sum 1,077,704

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #465587 ← → #465611

Radix Representation

Decimal	465600
Binary	1110001101011000000 (19 bits)
Octal	0o1615300
Hexadecimal	0x71AC0

Divisor Catalog (60 of 84)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 32 40 48 50 60 64 75 80 96 97 100 120 150 160 192 194 200 240 291 300 320 388 400 480 485 582 600 776 800 960 970 1,164 1,200 1,455 1,552 1,600 1,940 2,328 2,400 2,425 2,910 3,104 3,880 4,656 4,800

Collatz Trajectory (138 steps to reach 1)

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

465,600 232,800 116,400 58,200 29,100 14,550 7,275 21,826 10,913 32,740 16,370 8,185 24,556 12,278 6,139 18,418 9,209 27,628 13,814 6,907 20,722 10,361 31,084 15,542 7,771 23,314 11,657 34,972 17,486 8,743 26,230 13,115 39,346 19,673 59,020 29,510 14,755 44,266 22,133 66,400 33,200 16,600 8,300 4,150 2,075 6,226 3,113 9,340 4,670 2,335 7,006 3,503 10,510 5,255 15,766 7,883 23,650 11,825 35,476 17,738

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