405,180

2² × 3² × 5 × 2251

405,180 factors as 2^2 × 3^2 × 5 × 2251. Its 36 positive divisors give a proper-divisor sum of 824,412, so this integer is abundant. The Collatz stopping time is 112 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 2251

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 1,229,592

Proper Divisor Sum 824,412

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #405179 ← → #405199

Radix Representation

Decimal	405180
Binary	1100010111010111100 (19 bits)
Octal	0o1427274
Hexadecimal	0x62EBC

Divisor Catalog (36)

1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 2,251 4,502 6,753 9,004 11,255 13,506 20,259 22,510 27,012 33,765 40,518 45,020 67,530 81,036 101,295 135,060 202,590 405,180

Collatz Trajectory (112 steps to reach 1)

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

405,180 202,590 101,295 303,886 151,943 455,830 227,915 683,746 341,873 1,025,620 512,810 256,405 769,216 384,608 192,304 96,152 48,076 24,038 12,019 36,058 18,029 54,088 27,044 13,522 6,761 20,284 10,142 5,071 15,214 7,607 22,822 11,411 34,234 17,117 51,352 25,676 12,838 6,419 19,258 9,629 28,888 14,444 7,222 3,611 10,834 5,417 16,252 8,126 4,063 12,190 6,095 18,286 9,143 27,430 13,715 41,146 20,573 61,720 30,860 15,430

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