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Atlas › Integer Profiles › Node 6,810,760

6,810,760

23 × 5 × 11 × 23 × 673
Abundant Even Composite

6,810,760 factors as 2^3 × 5 × 11 × 23 × 673. Its 64 positive divisors give a proper-divisor sum of 10,659,320, so this integer is abundant. The Collatz stopping time is 116 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 11 × 23 × 673
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 17,470,080
Proper Divisor Sum 10,659,320
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #6810743 ← → #6810763

Radix Representation

Decimal 6810760
Binary 11001111110110010001000 (23 bits)
Octal 0o31766210
Hexadecimal 0x67EC88

Divisor Catalog (60 of 64)

1 2 4 5 8 10 11 20 22 23 40 44 46 55 88 92 110 115 184 220 230 253 440 460 506 673 920 1,012 1,265 1,346 2,024 2,530 2,692 3,365 5,060 5,384 6,730 7,403 10,120 13,460 14,806 15,479 26,920 29,612 30,958 37,015 59,224 61,916 74,030 77,395 123,832 148,060 154,790 170,269 296,120 309,580 340,538 619,160 681,076 851,345

Collatz Trajectory (116 steps to reach 1)

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

6,810,760 3,405,380 1,702,690 851,345 2,554,036 1,277,018 638,509 1,915,528 957,764 478,882 239,441 718,324 359,162 179,581 538,744 269,372 134,686 67,343 202,030 101,015 303,046 151,523 454,570 227,285 681,856 340,928 170,464 85,232 42,616 21,308 10,654 5,327 15,982 7,991 23,974 11,987 35,962 17,981 53,944 26,972 13,486 6,743 20,230 10,115 30,346 15,173 45,520 22,760 11,380 5,690 2,845 8,536 4,268 2,134 1,067 3,202 1,601 4,804 2,402 1,201

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