5,200,580

2² × 5 × 7 × 11² × 307

5,200,580 factors as 2^2 × 5 × 7 × 11^2 × 307. Its 72 positive divisors give a proper-divisor sum of 8,563,324, so this integer is abundant. The Collatz stopping time is 69 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 11^2 × 307

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 13,763,904

Proper Divisor Sum 8,563,324

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #5200579 ← → #5200627

Radix Representation

Decimal	5200580
Binary	10011110101101011000100 (23 bits)
Octal	0o23655304
Hexadecimal	0x4F5AC4

Divisor Catalog (60 of 72)

1 2 4 5 7 10 11 14 20 22 28 35 44 55 70 77 110 121 140 154 220 242 307 308 385 484 605 614 770 847 1,210 1,228 1,535 1,540 1,694 2,149 2,420 3,070 3,377 3,388 4,235 4,298 6,140 6,754 8,470 8,596 10,745 13,508 16,885 16,940 21,490 23,639 33,770 37,147 42,980 47,278 67,540 74,294 94,556 118,195

Collatz Trajectory (69 steps to reach 1)

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

5,200,580 2,600,290 1,300,145 3,900,436 1,950,218 975,109 2,925,328 1,462,664 731,332 365,666 182,833 548,500 274,250 137,125 411,376 205,688 102,844 51,422 25,711 77,134 38,567 115,702 57,851 173,554 86,777 260,332 130,166 65,083 195,250 97,625 292,876 146,438 73,219 219,658 109,829 329,488 164,744 82,372 41,186 20,593 61,780 30,890 15,445 46,336 23,168 11,584 5,792 2,896 1,448 724 362 181 544 272 136 68 34 17 52 26

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