361,200

2⁴ × 3 × 5² × 7 × 43

361,200 factors as 2^4 × 3 × 5^2 × 7 × 43. Its 120 positive divisors give a proper-divisor sum of 991,888, so this integer is abundant. The Collatz stopping time is 117 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5^2 × 7 × 43

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 1,353,088

Proper Divisor Sum 991,888

Digit Sum / Digital Root 12 (Root: 3)

Adjacent Primes #361183 ← → #361211

Radix Representation

Decimal	361200
Binary	1011000001011110000 (19 bits)
Octal	0o1301360
Hexadecimal	0x582F0

Divisor Catalog (60 of 120)

1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 25 28 30 35 40 42 43 48 50 56 60 70 75 80 84 86 100 105 112 120 129 140 150 168 172 175 200 210 215 240 258 280 300 301 336 344 350 400 420 430 516 525 560 600

Collatz Trajectory (117 steps to reach 1)

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

361,200 180,600 90,300 45,150 22,575 67,726 33,863 101,590 50,795 152,386 76,193 228,580 114,290 57,145 171,436 85,718 42,859 128,578 64,289 192,868 96,434 48,217 144,652 72,326 36,163 108,490 54,245 162,736 81,368 40,684 20,342 10,171 30,514 15,257 45,772 22,886 11,443 34,330 17,165 51,496 25,748 12,874 6,437 19,312 9,656 4,828 2,414 1,207 3,622 1,811 5,434 2,717 8,152 4,076 2,038 1,019 3,058 1,529 4,588 2,294

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