1,300,320

2⁵ × 3³ × 5 × 7 × 43

1,300,320 factors as 2^5 × 3^3 × 5 × 7 × 43. Its 192 positive divisors give a proper-divisor sum of 4,021,920, so this integer is abundant. The Collatz stopping time is 186 steps.

Prime Factor Structure

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

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 192

Divisor Sum (σ) 5,322,240

Proper Divisor Sum 4,021,920

Digit Sum / Digital Root 9 (Root: 9)

Adjacent Primes #1300319 ← → #1300333

Radix Representation

Decimal	1300320
Binary	100111101011101100000 (21 bits)
Octal	0o4753540
Hexadecimal	0x13D760

Divisor Catalog (60 of 192)

1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 27 28 30 32 35 36 40 42 43 45 48 54 56 60 63 70 72 80 84 86 90 96 105 108 112 120 126 129 135 140 144 160 168 172 180 189 210 215 216 224 240 252

Collatz Trajectory (186 steps to reach 1)

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

1,300,320 650,160 325,080 162,540 81,270 40,635 121,906 60,953 182,860 91,430 45,715 137,146 68,573 205,720 102,860 51,430 25,715 77,146 38,573 115,720 57,860 28,930 14,465 43,396 21,698 10,849 32,548 16,274 8,137 24,412 12,206 6,103 18,310 9,155 27,466 13,733 41,200 20,600 10,300 5,150 2,575 7,726 3,863 11,590 5,795 17,386 8,693 26,080 13,040 6,520 3,260 1,630 815 2,446 1,223 3,670 1,835 5,506 2,753 8,260

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