5,199,840

2⁵ × 3² × 5 × 23 × 157

5,199,840 factors as 2^5 × 3^2 × 5 × 23 × 157. Its 144 positive divisors give a proper-divisor sum of 13,434,048, so this integer is abundant. The Collatz stopping time is 206 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 23 × 157

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 18,633,888

Proper Divisor Sum 13,434,048

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #5199829 ← → #5199853

Radix Representation

Decimal	5199840
Binary	10011110101011111100000 (23 bits)
Octal	0o23653740
Hexadecimal	0x4F57E0

Divisor Catalog (60 of 144)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 23 24 30 32 36 40 45 46 48 60 69 72 80 90 92 96 115 120 138 144 157 160 180 184 207 230 240 276 288 314 345 360 368 414 460 471 480 552 628 690 720 736 785 828 920 942

Collatz Trajectory (206 steps to reach 1)

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

5,199,840 2,599,920 1,299,960 649,980 324,990 162,495 487,486 243,743 731,230 365,615 1,096,846 548,423 1,645,270 822,635 2,467,906 1,233,953 3,701,860 1,850,930 925,465 2,776,396 1,388,198 694,099 2,082,298 1,041,149 3,123,448 1,561,724 780,862 390,431 1,171,294 585,647 1,756,942 878,471 2,635,414 1,317,707 3,953,122 1,976,561 5,929,684 2,964,842 1,482,421 4,447,264 2,223,632 1,111,816 555,908 277,954 138,977 416,932 208,466 104,233 312,700 156,350 78,175 234,526 117,263 351,790 175,895 527,686 263,843 791,530 395,765 1,187,296

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