λ
Harmonic Matrix

6,840,180

22 × 33 × 5 × 53 × 239
Abundant Even Composite

6,840,180 has digital root 9. The neighboring primes are 6840179 and 6840187; its proper-divisor sum differs from the starting integer by 8,092,440.

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Prime Factor Structure

Factorization String 2^2 × 3^3 × 5 × 53 × 239
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 96
Divisor Sum (σ) 21,772,800
Proper Divisor Sum 14,932,620
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #6840179 ← → #6840187

Radix Representation

Decimal 6840180
Binary 11010000101111101110100 (23 bits)
Octal 0o32057564
Hexadecimal 0x685F74

Divisor Catalog (5 of 96)

1 2 3 4 5

Collatz Trajectory (222 steps to reach 1)

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

Showing the first 5 trajectory entries; the stopping-time total above is unchanged.

6,840,180 3,420,090 1,710,045 5,130,136 2,565,068

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