9,999,600

2⁴ × 3 × 5² × 13 × 641

9,999,600 factors as 2^4 × 3 × 5^2 × 13 × 641. Its 120 positive divisors give a proper-divisor sum of 24,550,272, so this integer is abundant. The Collatz stopping time is 220 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5^2 × 13 × 641

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 34,549,872

Proper Divisor Sum 24,550,272

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #9999593 ← → #9999601

Radix Representation

Decimal	9999600
Binary	100110001001010011110000 (24 bits)
Octal	0o46112360
Hexadecimal	0x9894F0

Divisor Catalog (60 of 120)

1 2 3 4 5 6 8 10 12 13 15 16 20 24 25 26 30 39 40 48 50 52 60 65 75 78 80 100 104 120 130 150 156 195 200 208 240 260 300 312 325 390 400 520 600 624 641 650 780 975 1,040 1,200 1,282 1,300 1,560 1,923 1,950 2,564 2,600 3,120

Collatz Trajectory (220 steps to reach 1)

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

9,999,600 4,999,800 2,499,900 1,249,950 624,975 1,874,926 937,463 2,812,390 1,406,195 4,218,586 2,109,293 6,327,880 3,163,940 1,581,970 790,985 2,372,956 1,186,478 593,239 1,779,718 889,859 2,669,578 1,334,789 4,004,368 2,002,184 1,001,092 500,546 250,273 750,820 375,410 187,705 563,116 281,558 140,779 422,338 211,169 633,508 316,754 158,377 475,132 237,566 118,783 356,350 178,175 534,526 267,263 801,790 400,895 1,202,686 601,343 1,804,030 902,015 2,706,046 1,353,023 4,059,070 2,029,535 6,088,606 3,044,303 9,132,910 4,566,455 13,699,366

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