λ
Harmonic Matrix

6,827,140

22 × 5 × 341357
Abundant Even Composite

6,827,140 has digital root 1. The neighboring primes are 6827131 and 6827141; its proper-divisor sum differs from the starting integer by 682,756.

Prime Factor Structure

Factorization String 2^2 × 5 × 341357
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 14,337,036
Proper Divisor Sum 7,509,896
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #6827131 ← → #6827141

Radix Representation

Decimal 6827140
Binary 11010000010110010000100 (23 bits)
Octal 0o32026204
Hexadecimal 0x682C84

Divisor Catalog (12)

1 2 4 5 10 20 341,357 682,714 1,365,428 1,706,785 3,413,570 6,827,140

Collatz Trajectory (103 steps to reach 1)

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

6,827,140 3,413,570 1,706,785 5,120,356 2,560,178 1,280,089 3,840,268 1,920,134 960,067 2,880,202 1,440,101 4,320,304 2,160,152 1,080,076 540,038 270,019 810,058 405,029 1,215,088 607,544 303,772 151,886 75,943 227,830 113,915 341,746 170,873 512,620 256,310 128,155 384,466 192,233 576,700 288,350 144,175 432,526 216,263 648,790 324,395 973,186 486,593 1,459,780 729,890 364,945 1,094,836 547,418 273,709 821,128 410,564 205,282 102,641 307,924 153,962 76,981 230,944 115,472 57,736 28,868 14,434 7,217

More profiles

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