8,513,680

2⁴ × 5 × 7 × 23 × 661

8,513,680 factors as 2^4 × 5 × 7 × 23 × 661. Its 80 positive divisors give a proper-divisor sum of 15,127,664, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 23 × 661

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 23,641,344

Proper Divisor Sum 15,127,664

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #8513677 ← → #8513683

Radix Representation

Decimal	8513680
Binary	100000011110100010010000 (24 bits)
Octal	0o40364220
Hexadecimal	0x81E890

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 23 28 35 40 46 56 70 80 92 112 115 140 161 184 230 280 322 368 460 560 644 661 805 920 1,288 1,322 1,610 1,840 2,576 2,644 3,220 3,305 4,627 5,288 6,440 6,610 9,254 10,576 12,880 13,220 15,203 18,508 23,135 26,440 30,406 37,016 46,270 52,880 60,812 74,032

Collatz Trajectory (199 steps to reach 1)

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

8,513,680 4,256,840 2,128,420 1,064,210 532,105 1,596,316 798,158 399,079 1,197,238 598,619 1,795,858 897,929 2,693,788 1,346,894 673,447 2,020,342 1,010,171 3,030,514 1,515,257 4,545,772 2,272,886 1,136,443 3,409,330 1,704,665 5,113,996 2,556,998 1,278,499 3,835,498 1,917,749 5,753,248 2,876,624 1,438,312 719,156 359,578 179,789 539,368 269,684 134,842 67,421 202,264 101,132 50,566 25,283 75,850 37,925 113,776 56,888 28,444 14,222 7,111 21,334 10,667 32,002 16,001 48,004 24,002 12,001 36,004 18,002 9,001

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